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27 | <a name="math_toolkit.tr1_ref"></a><a class="link" href="tr1_ref.html" title="TR1 C Functions Quick Reference">TR1 C Functions Quick Reference</a> | |
28 | </h2></div></div></div> | |
29 | <h5> | |
30 | <a name="math_toolkit.tr1_ref.h0"></a> | |
31 | <span class="phrase"><a name="math_toolkit.tr1_ref.supported_tr1_functions"></a></span><a class="link" href="tr1_ref.html#math_toolkit.tr1_ref.supported_tr1_functions">Supported | |
32 | TR1 Functions</a> | |
33 | </h5> | |
34 | <pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">tr1</span><span class="special">{</span> <span class="keyword">extern</span> <span class="string">"C"</span><span class="special">{</span> | |
35 | ||
36 | <span class="comment">// [5.2.1.1] associated Laguerre polynomials:</span> | |
37 | <span class="keyword">double</span> <span class="identifier">assoc_laguerre</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">n</span><span class="special">,</span> <span class="keyword">unsigned</span> <span class="identifier">m</span><span class="special">,</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span> | |
38 | <span class="keyword">float</span> <span class="identifier">assoc_laguerref</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">n</span><span class="special">,</span> <span class="keyword">unsigned</span> <span class="identifier">m</span><span class="special">,</span> <span class="keyword">float</span> <span class="identifier">x</span><span class="special">);</span> | |
39 | <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">assoc_laguerrel</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">n</span><span class="special">,</span> <span class="keyword">unsigned</span> <span class="identifier">m</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span> | |
40 | ||
41 | <span class="comment">// [5.2.1.2] associated Legendre functions:</span> | |
42 | <span class="keyword">double</span> <span class="identifier">assoc_legendre</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">l</span><span class="special">,</span> <span class="keyword">unsigned</span> <span class="identifier">m</span><span class="special">,</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span> | |
43 | <span class="keyword">float</span> <span class="identifier">assoc_legendref</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">l</span><span class="special">,</span> <span class="keyword">unsigned</span> <span class="identifier">m</span><span class="special">,</span> <span class="keyword">float</span> <span class="identifier">x</span><span class="special">);</span> | |
44 | <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">assoc_legendrel</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">l</span><span class="special">,</span> <span class="keyword">unsigned</span> <span class="identifier">m</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span> | |
45 | ||
46 | <span class="comment">// [5.2.1.3] beta function:</span> | |
47 | <span class="keyword">double</span> <span class="identifier">beta</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">double</span> <span class="identifier">y</span><span class="special">);</span> | |
48 | <span class="keyword">float</span> <span class="identifier">betaf</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">float</span> <span class="identifier">y</span><span class="special">);</span> | |
49 | <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">betal</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">y</span><span class="special">);</span> | |
50 | ||
51 | <span class="comment">// [5.2.1.4] (complete) elliptic integral of the first kind:</span> | |
52 | <span class="keyword">double</span> <span class="identifier">comp_ellint_1</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">k</span><span class="special">);</span> | |
53 | <span class="keyword">float</span> <span class="identifier">comp_ellint_1f</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">k</span><span class="special">);</span> | |
54 | <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">comp_ellint_1l</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">k</span><span class="special">);</span> | |
55 | ||
56 | <span class="comment">// [5.2.1.5] (complete) elliptic integral of the second kind:</span> | |
57 | <span class="keyword">double</span> <span class="identifier">comp_ellint_2</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">k</span><span class="special">);</span> | |
58 | <span class="keyword">float</span> <span class="identifier">comp_ellint_2f</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">k</span><span class="special">);</span> | |
59 | <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">comp_ellint_2l</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">k</span><span class="special">);</span> | |
60 | ||
61 | <span class="comment">// [5.2.1.6] (complete) elliptic integral of the third kind:</span> | |
62 | <span class="keyword">double</span> <span class="identifier">comp_ellint_3</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">k</span><span class="special">,</span> <span class="keyword">double</span> <span class="identifier">nu</span><span class="special">);</span> | |
63 | <span class="keyword">float</span> <span class="identifier">comp_ellint_3f</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">k</span><span class="special">,</span> <span class="keyword">float</span> <span class="identifier">nu</span><span class="special">);</span> | |
64 | <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">comp_ellint_3l</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">k</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">nu</span><span class="special">);</span> | |
65 | ||
66 | <span class="comment">// [5.2.1.8] regular modified cylindrical Bessel functions:</span> | |
67 | <span class="keyword">double</span> <span class="identifier">cyl_bessel_i</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">nu</span><span class="special">,</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span> | |
68 | <span class="keyword">float</span> <span class="identifier">cyl_bessel_if</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">nu</span><span class="special">,</span> <span class="keyword">float</span> <span class="identifier">x</span><span class="special">);</span> | |
69 | <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">cyl_bessel_il</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">nu</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span> | |
70 | ||
71 | <span class="comment">// [5.2.1.9] cylindrical Bessel functions (of the first kind):</span> | |
72 | <span class="keyword">double</span> <span class="identifier">cyl_bessel_j</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">nu</span><span class="special">,</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span> | |
73 | <span class="keyword">float</span> <span class="identifier">cyl_bessel_jf</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">nu</span><span class="special">,</span> <span class="keyword">float</span> <span class="identifier">x</span><span class="special">);</span> | |
74 | <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">cyl_bessel_jl</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">nu</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span> | |
75 | ||
76 | <span class="comment">// [5.2.1.10] irregular modified cylindrical Bessel functions:</span> | |
77 | <span class="keyword">double</span> <span class="identifier">cyl_bessel_k</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">nu</span><span class="special">,</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span> | |
78 | <span class="keyword">float</span> <span class="identifier">cyl_bessel_kf</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">nu</span><span class="special">,</span> <span class="keyword">float</span> <span class="identifier">x</span><span class="special">);</span> | |
79 | <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">cyl_bessel_kl</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">nu</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span> | |
80 | ||
81 | <span class="comment">// [5.2.1.11] cylindrical Neumann functions;</span> | |
82 | <span class="comment">// cylindrical Bessel functions (of the second kind):</span> | |
83 | <span class="keyword">double</span> <span class="identifier">cyl_neumann</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">nu</span><span class="special">,</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span> | |
84 | <span class="keyword">float</span> <span class="identifier">cyl_neumannf</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">nu</span><span class="special">,</span> <span class="keyword">float</span> <span class="identifier">x</span><span class="special">);</span> | |
85 | <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">cyl_neumannl</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">nu</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span> | |
86 | ||
87 | <span class="comment">// [5.2.1.12] (incomplete) elliptic integral of the first kind:</span> | |
88 | <span class="keyword">double</span> <span class="identifier">ellint_1</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">k</span><span class="special">,</span> <span class="keyword">double</span> <span class="identifier">phi</span><span class="special">);</span> | |
89 | <span class="keyword">float</span> <span class="identifier">ellint_1f</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">k</span><span class="special">,</span> <span class="keyword">float</span> <span class="identifier">phi</span><span class="special">);</span> | |
90 | <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">ellint_1l</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">k</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">phi</span><span class="special">);</span> | |
91 | ||
92 | <span class="comment">// [5.2.1.13] (incomplete) elliptic integral of the second kind:</span> | |
93 | <span class="keyword">double</span> <span class="identifier">ellint_2</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">k</span><span class="special">,</span> <span class="keyword">double</span> <span class="identifier">phi</span><span class="special">);</span> | |
94 | <span class="keyword">float</span> <span class="identifier">ellint_2f</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">k</span><span class="special">,</span> <span class="keyword">float</span> <span class="identifier">phi</span><span class="special">);</span> | |
95 | <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">ellint_2l</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">k</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">phi</span><span class="special">);</span> | |
96 | ||
97 | <span class="comment">// [5.2.1.14] (incomplete) elliptic integral of the third kind:</span> | |
98 | <span class="keyword">double</span> <span class="identifier">ellint_3</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">k</span><span class="special">,</span> <span class="keyword">double</span> <span class="identifier">nu</span><span class="special">,</span> <span class="keyword">double</span> <span class="identifier">phi</span><span class="special">);</span> | |
99 | <span class="keyword">float</span> <span class="identifier">ellint_3f</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">k</span><span class="special">,</span> <span class="keyword">float</span> <span class="identifier">nu</span><span class="special">,</span> <span class="keyword">float</span> <span class="identifier">phi</span><span class="special">);</span> | |
100 | <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">ellint_3l</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">k</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">nu</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">phi</span><span class="special">);</span> | |
101 | ||
102 | <span class="comment">// [5.2.1.15] exponential integral:</span> | |
103 | <span class="keyword">double</span> <span class="identifier">expint</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span> | |
104 | <span class="keyword">float</span> <span class="identifier">expintf</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">x</span><span class="special">);</span> | |
105 | <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">expintl</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span> | |
106 | ||
107 | <span class="comment">// [5.2.1.16] Hermite polynomials:</span> | |
108 | <span class="keyword">double</span> <span class="identifier">hermite</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">n</span><span class="special">,</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span> | |
109 | <span class="keyword">float</span> <span class="identifier">hermitef</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">n</span><span class="special">,</span> <span class="keyword">float</span> <span class="identifier">x</span><span class="special">);</span> | |
110 | <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">hermitel</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">n</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span> | |
111 | ||
112 | <span class="comment">// [5.2.1.18] Laguerre polynomials:</span> | |
113 | <span class="keyword">double</span> <span class="identifier">laguerre</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">n</span><span class="special">,</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span> | |
114 | <span class="keyword">float</span> <span class="identifier">laguerref</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">n</span><span class="special">,</span> <span class="keyword">float</span> <span class="identifier">x</span><span class="special">);</span> | |
115 | <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">laguerrel</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">n</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span> | |
116 | ||
117 | <span class="comment">// [5.2.1.19] Legendre polynomials:</span> | |
118 | <span class="keyword">double</span> <span class="identifier">legendre</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">l</span><span class="special">,</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span> | |
119 | <span class="keyword">float</span> <span class="identifier">legendref</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">l</span><span class="special">,</span> <span class="keyword">float</span> <span class="identifier">x</span><span class="special">);</span> | |
120 | <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">legendrel</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">l</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span> | |
121 | ||
122 | <span class="comment">// [5.2.1.20] Riemann zeta function:</span> | |
123 | <span class="keyword">double</span> <span class="identifier">riemann_zeta</span><span class="special">(</span><span class="keyword">double</span><span class="special">);</span> | |
124 | <span class="keyword">float</span> <span class="identifier">riemann_zetaf</span><span class="special">(</span><span class="keyword">float</span><span class="special">);</span> | |
125 | <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">riemann_zetal</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">);</span> | |
126 | ||
127 | <span class="comment">// [5.2.1.21] spherical Bessel functions (of the first kind):</span> | |
128 | <span class="keyword">double</span> <span class="identifier">sph_bessel</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">n</span><span class="special">,</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span> | |
129 | <span class="keyword">float</span> <span class="identifier">sph_besself</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">n</span><span class="special">,</span> <span class="keyword">float</span> <span class="identifier">x</span><span class="special">);</span> | |
130 | <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">sph_bessell</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">n</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span> | |
131 | ||
132 | <span class="comment">// [5.2.1.22] spherical associated Legendre functions:</span> | |
133 | <span class="keyword">double</span> <span class="identifier">sph_legendre</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">l</span><span class="special">,</span> <span class="keyword">unsigned</span> <span class="identifier">m</span><span class="special">,</span> <span class="keyword">double</span> <span class="identifier">theta</span><span class="special">);</span> | |
134 | <span class="keyword">float</span> <span class="identifier">sph_legendref</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">l</span><span class="special">,</span> <span class="keyword">unsigned</span> <span class="identifier">m</span><span class="special">,</span> <span class="keyword">float</span> <span class="identifier">theta</span><span class="special">);</span> | |
135 | <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">sph_legendrel</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">l</span><span class="special">,</span> <span class="keyword">unsigned</span> <span class="identifier">m</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">theta</span><span class="special">);</span> | |
136 | ||
137 | <span class="comment">// [5.2.1.23] spherical Neumann functions;</span> | |
138 | <span class="comment">// spherical Bessel functions (of the second kind):</span> | |
139 | <span class="keyword">double</span> <span class="identifier">sph_neumann</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">n</span><span class="special">,</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span> | |
140 | <span class="keyword">float</span> <span class="identifier">sph_neumannf</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">n</span><span class="special">,</span> <span class="keyword">float</span> <span class="identifier">x</span><span class="special">);</span> | |
141 | <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">sph_neumannl</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">n</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span> | |
142 | ||
143 | <span class="special">}}}}</span> <span class="comment">// namespaces</span> | |
144 | </pre> | |
145 | <p> | |
146 | In addition sufficient additional overloads of the <code class="computeroutput"><span class="keyword">double</span></code> | |
147 | versions of the above functions are provided, so that calling the function | |
148 | with any mixture of <code class="computeroutput"><span class="keyword">float</span></code>, <code class="computeroutput"><span class="keyword">double</span></code>, <code class="computeroutput"><span class="keyword">long</span> | |
149 | <span class="keyword">double</span></code>, or <span class="emphasis"><em>integer</em></span> | |
150 | arguments is supported, with the return type determined by the <a class="link" href="result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>result | |
151 | type calculation rules</em></span></a>. | |
152 | </p> | |
153 | <p> | |
154 | For example: | |
155 | </p> | |
156 | <pre class="programlisting"><span class="identifier">expintf</span><span class="special">(</span><span class="number">2.0f</span><span class="special">);</span> <span class="comment">// float version, returns float.</span> | |
157 | <span class="identifier">expint</span><span class="special">(</span><span class="number">2.0f</span><span class="special">);</span> <span class="comment">// also calls the float version and returns float.</span> | |
158 | <span class="identifier">expint</span><span class="special">(</span><span class="number">2.0</span><span class="special">);</span> <span class="comment">// double version, returns double.</span> | |
159 | <span class="identifier">expintl</span><span class="special">(</span><span class="number">2.0L</span><span class="special">);</span> <span class="comment">// long double version, returns a long double.</span> | |
160 | <span class="identifier">expint</span><span class="special">(</span><span class="number">2.0L</span><span class="special">);</span> <span class="comment">// also calls the long double version.</span> | |
161 | <span class="identifier">expint</span><span class="special">(</span><span class="number">2</span><span class="special">);</span> <span class="comment">// integer argument is treated as a double, returns double.</span> | |
162 | </pre> | |
163 | <h5> | |
164 | <a name="math_toolkit.tr1_ref.h1"></a> | |
165 | <span class="phrase"><a name="math_toolkit.tr1_ref.quick_reference"></a></span><a class="link" href="tr1_ref.html#math_toolkit.tr1_ref.quick_reference">Quick | |
166 | Reference</a> | |
167 | </h5> | |
168 | <pre class="programlisting"><span class="comment">// [5.2.1.1] associated Laguerre polynomials:</span> | |
169 | <span class="keyword">double</span> <span class="identifier">assoc_laguerre</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">n</span><span class="special">,</span> <span class="keyword">unsigned</span> <span class="identifier">m</span><span class="special">,</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span> | |
170 | <span class="keyword">float</span> <span class="identifier">assoc_laguerref</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">n</span><span class="special">,</span> <span class="keyword">unsigned</span> <span class="identifier">m</span><span class="special">,</span> <span class="keyword">float</span> <span class="identifier">x</span><span class="special">);</span> | |
171 | <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">assoc_laguerrel</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">n</span><span class="special">,</span> <span class="keyword">unsigned</span> <span class="identifier">m</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span> | |
172 | </pre> | |
173 | <p> | |
174 | The assoc_laguerre functions return: | |
175 | </p> | |
176 | <p> | |
177 | <span class="inlinemediaobject"><img src="../../equations/laguerre_1.svg"></span> | |
178 | </p> | |
179 | <p> | |
180 | See also <a class="link" href="sf_poly/laguerre.html" title="Laguerre (and Associated) Polynomials">laguerre</a> for | |
181 | the full template (header only) version of this function. | |
182 | </p> | |
183 | <pre class="programlisting"><span class="comment">// [5.2.1.2] associated Legendre functions:</span> | |
184 | <span class="keyword">double</span> <span class="identifier">assoc_legendre</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">l</span><span class="special">,</span> <span class="keyword">unsigned</span> <span class="identifier">m</span><span class="special">,</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span> | |
185 | <span class="keyword">float</span> <span class="identifier">assoc_legendref</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">l</span><span class="special">,</span> <span class="keyword">unsigned</span> <span class="identifier">m</span><span class="special">,</span> <span class="keyword">float</span> <span class="identifier">x</span><span class="special">);</span> | |
186 | <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">assoc_legendrel</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">l</span><span class="special">,</span> <span class="keyword">unsigned</span> <span class="identifier">m</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span> | |
187 | </pre> | |
188 | <p> | |
189 | The assoc_legendre functions return: | |
190 | </p> | |
191 | <p> | |
192 | <span class="inlinemediaobject"><img src="../../equations/legendre_1b.svg"></span> | |
193 | </p> | |
194 | <p> | |
195 | See also <a class="link" href="sf_poly/legendre.html" title="Legendre (and Associated) Polynomials">legendre_p</a> for | |
196 | the full template (header only) version of this function. | |
197 | </p> | |
198 | <pre class="programlisting"><span class="comment">// [5.2.1.3] beta function:</span> | |
199 | <span class="keyword">double</span> <span class="identifier">beta</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">double</span> <span class="identifier">y</span><span class="special">);</span> | |
200 | <span class="keyword">float</span> <span class="identifier">betaf</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">float</span> <span class="identifier">y</span><span class="special">);</span> | |
201 | <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">betal</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">y</span><span class="special">);</span> | |
202 | </pre> | |
203 | <p> | |
204 | Returns the beta function of <span class="emphasis"><em>x</em></span> and <span class="emphasis"><em>y</em></span>: | |
205 | </p> | |
206 | <p> | |
207 | <span class="inlinemediaobject"><img src="../../equations/beta1.svg"></span> | |
208 | </p> | |
209 | <p> | |
210 | See also <a class="link" href="sf_beta/beta_function.html" title="Beta">beta</a> for | |
211 | the full template (header only) version of this function. | |
212 | </p> | |
213 | <pre class="programlisting"><span class="comment">// [5.2.1.4] (complete) elliptic integral of the first kind:</span> | |
214 | <span class="keyword">double</span> <span class="identifier">comp_ellint_1</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">k</span><span class="special">);</span> | |
215 | <span class="keyword">float</span> <span class="identifier">comp_ellint_1f</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">k</span><span class="special">);</span> | |
216 | <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">comp_ellint_1l</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">k</span><span class="special">);</span> | |
217 | </pre> | |
218 | <p> | |
219 | Returns the complete elliptic integral of the first kind of <span class="emphasis"><em>k</em></span>: | |
220 | </p> | |
221 | <p> | |
222 | <span class="inlinemediaobject"><img src="../../equations/ellint6.svg"></span> | |
223 | </p> | |
224 | <p> | |
225 | See also <a class="link" href="ellint/ellint_1.html" title="Elliptic Integrals of the First Kind - Legendre Form">ellint_1</a> for the | |
226 | full template (header only) version of this function. | |
227 | </p> | |
228 | <pre class="programlisting"><span class="comment">// [5.2.1.5] (complete) elliptic integral of the second kind:</span> | |
229 | <span class="keyword">double</span> <span class="identifier">comp_ellint_2</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">k</span><span class="special">);</span> | |
230 | <span class="keyword">float</span> <span class="identifier">comp_ellint_2f</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">k</span><span class="special">);</span> | |
231 | <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">comp_ellint_2l</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">k</span><span class="special">);</span> | |
232 | </pre> | |
233 | <p> | |
234 | Returns the complete elliptic integral of the second kind of <span class="emphasis"><em>k</em></span>: | |
235 | </p> | |
236 | <p> | |
237 | <span class="inlinemediaobject"><img src="../../equations/ellint7.svg"></span> | |
238 | </p> | |
239 | <p> | |
240 | See also <a class="link" href="ellint/ellint_2.html" title="Elliptic Integrals of the Second Kind - Legendre Form">ellint_2</a> for the | |
241 | full template (header only) version of this function. | |
242 | </p> | |
243 | <pre class="programlisting"><span class="comment">// [5.2.1.6] (complete) elliptic integral of the third kind:</span> | |
244 | <span class="keyword">double</span> <span class="identifier">comp_ellint_3</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">k</span><span class="special">,</span> <span class="keyword">double</span> <span class="identifier">nu</span><span class="special">);</span> | |
245 | <span class="keyword">float</span> <span class="identifier">comp_ellint_3f</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">k</span><span class="special">,</span> <span class="keyword">float</span> <span class="identifier">nu</span><span class="special">);</span> | |
246 | <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">comp_ellint_3l</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">k</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">nu</span><span class="special">);</span> | |
247 | </pre> | |
248 | <p> | |
249 | Returns the complete elliptic integral of the third kind of <span class="emphasis"><em>k</em></span> | |
250 | and <span class="emphasis"><em>nu</em></span>: | |
251 | </p> | |
252 | <p> | |
253 | <span class="inlinemediaobject"><img src="../../equations/ellint8.svg"></span> | |
254 | </p> | |
255 | <p> | |
256 | See also <a class="link" href="ellint/ellint_3.html" title="Elliptic Integrals of the Third Kind - Legendre Form">ellint_3</a> for the | |
257 | full template (header only) version of this function. | |
258 | </p> | |
259 | <pre class="programlisting"><span class="comment">// [5.2.1.8] regular modified cylindrical Bessel functions:</span> | |
260 | <span class="keyword">double</span> <span class="identifier">cyl_bessel_i</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">nu</span><span class="special">,</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span> | |
261 | <span class="keyword">float</span> <span class="identifier">cyl_bessel_if</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">nu</span><span class="special">,</span> <span class="keyword">float</span> <span class="identifier">x</span><span class="special">);</span> | |
262 | <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">cyl_bessel_il</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">nu</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span> | |
263 | </pre> | |
264 | <p> | |
265 | Returns the modified bessel function of the first kind of <span class="emphasis"><em>nu</em></span> | |
266 | and <span class="emphasis"><em>x</em></span>: | |
267 | </p> | |
268 | <p> | |
269 | <span class="inlinemediaobject"><img src="../../equations/mbessel2.svg"></span> | |
270 | </p> | |
271 | <p> | |
272 | See also <a class="link" href="bessel/mbessel.html" title="Modified Bessel Functions of the First and Second Kinds">cyl_bessel_i</a> for | |
273 | the full template (header only) version of this function. | |
274 | </p> | |
275 | <pre class="programlisting"><span class="comment">// [5.2.1.9] cylindrical Bessel functions (of the first kind):</span> | |
276 | <span class="keyword">double</span> <span class="identifier">cyl_bessel_j</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">nu</span><span class="special">,</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span> | |
277 | <span class="keyword">float</span> <span class="identifier">cyl_bessel_jf</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">nu</span><span class="special">,</span> <span class="keyword">float</span> <span class="identifier">x</span><span class="special">);</span> | |
278 | <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">cyl_bessel_jl</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">nu</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span> | |
279 | </pre> | |
280 | <p> | |
281 | Returns the bessel function of the first kind of <span class="emphasis"><em>nu</em></span> and | |
282 | <span class="emphasis"><em>x</em></span>: | |
283 | </p> | |
284 | <p> | |
285 | <span class="inlinemediaobject"><img src="../../equations/bessel2.svg"></span> | |
286 | </p> | |
287 | <p> | |
288 | See also <a class="link" href="bessel/bessel_first.html" title="Bessel Functions of the First and Second Kinds">cyl_bessel_j</a> | |
289 | for the full template (header only) version of this function. | |
290 | </p> | |
291 | <pre class="programlisting"><span class="comment">// [5.2.1.10] irregular modified cylindrical Bessel functions:</span> | |
292 | <span class="keyword">double</span> <span class="identifier">cyl_bessel_k</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">nu</span><span class="special">,</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span> | |
293 | <span class="keyword">float</span> <span class="identifier">cyl_bessel_kf</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">nu</span><span class="special">,</span> <span class="keyword">float</span> <span class="identifier">x</span><span class="special">);</span> | |
294 | <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">cyl_bessel_kl</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">nu</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span> | |
295 | </pre> | |
296 | <p> | |
297 | Returns the modified bessel function of the second kind of <span class="emphasis"><em>nu</em></span> | |
298 | and <span class="emphasis"><em>x</em></span>: | |
299 | </p> | |
300 | <p> | |
301 | <span class="inlinemediaobject"><img src="../../equations/mbessel3.svg"></span> | |
302 | </p> | |
303 | <p> | |
304 | See also <a class="link" href="bessel/mbessel.html" title="Modified Bessel Functions of the First and Second Kinds">cyl_bessel_k</a> for | |
305 | the full template (header only) version of this function. | |
306 | </p> | |
307 | <pre class="programlisting"><span class="comment">// [5.2.1.11] cylindrical Neumann functions;</span> | |
308 | <span class="comment">// cylindrical Bessel functions (of the second kind):</span> | |
309 | <span class="keyword">double</span> <span class="identifier">cyl_neumann</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">nu</span><span class="special">,</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span> | |
310 | <span class="keyword">float</span> <span class="identifier">cyl_neumannf</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">nu</span><span class="special">,</span> <span class="keyword">float</span> <span class="identifier">x</span><span class="special">);</span> | |
311 | <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">cyl_neumannl</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">nu</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span> | |
312 | </pre> | |
313 | <p> | |
314 | Returns the bessel function of the second kind (Neumann function) of <span class="emphasis"><em>nu</em></span> | |
315 | and <span class="emphasis"><em>x</em></span>: | |
316 | </p> | |
317 | <p> | |
318 | <span class="inlinemediaobject"><img src="../../equations/bessel3.svg"></span> | |
319 | </p> | |
320 | <p> | |
321 | See also <a class="link" href="bessel/bessel_first.html" title="Bessel Functions of the First and Second Kinds">cyl_neumann</a> | |
322 | for the full template (header only) version of this function. | |
323 | </p> | |
324 | <pre class="programlisting"><span class="comment">// [5.2.1.12] (incomplete) elliptic integral of the first kind:</span> | |
325 | <span class="keyword">double</span> <span class="identifier">ellint_1</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">k</span><span class="special">,</span> <span class="keyword">double</span> <span class="identifier">phi</span><span class="special">);</span> | |
326 | <span class="keyword">float</span> <span class="identifier">ellint_1f</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">k</span><span class="special">,</span> <span class="keyword">float</span> <span class="identifier">phi</span><span class="special">);</span> | |
327 | <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">ellint_1l</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">k</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">phi</span><span class="special">);</span> | |
328 | </pre> | |
329 | <p> | |
330 | Returns the incomplete elliptic integral of the first kind of <span class="emphasis"><em>k</em></span> | |
331 | and <span class="emphasis"><em>phi</em></span>: | |
332 | </p> | |
333 | <p> | |
334 | <span class="inlinemediaobject"><img src="../../equations/ellint2.svg"></span> | |
335 | </p> | |
336 | <p> | |
337 | See also <a class="link" href="ellint/ellint_1.html" title="Elliptic Integrals of the First Kind - Legendre Form">ellint_1</a> for the | |
338 | full template (header only) version of this function. | |
339 | </p> | |
340 | <pre class="programlisting"><span class="comment">// [5.2.1.13] (incomplete) elliptic integral of the second kind:</span> | |
341 | <span class="keyword">double</span> <span class="identifier">ellint_2</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">k</span><span class="special">,</span> <span class="keyword">double</span> <span class="identifier">phi</span><span class="special">);</span> | |
342 | <span class="keyword">float</span> <span class="identifier">ellint_2f</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">k</span><span class="special">,</span> <span class="keyword">float</span> <span class="identifier">phi</span><span class="special">);</span> | |
343 | <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">ellint_2l</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">k</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">phi</span><span class="special">);</span> | |
344 | </pre> | |
345 | <p> | |
346 | Returns the incomplete elliptic integral of the second kind of <span class="emphasis"><em>k</em></span> | |
347 | and <span class="emphasis"><em>phi</em></span>: | |
348 | </p> | |
349 | <p> | |
350 | <span class="inlinemediaobject"><img src="../../equations/ellint3.svg"></span> | |
351 | </p> | |
352 | <p> | |
353 | See also <a class="link" href="ellint/ellint_2.html" title="Elliptic Integrals of the Second Kind - Legendre Form">ellint_2</a> for the | |
354 | full template (header only) version of this function. | |
355 | </p> | |
356 | <pre class="programlisting"><span class="comment">// [5.2.1.14] (incomplete) elliptic integral of the third kind:</span> | |
357 | <span class="keyword">double</span> <span class="identifier">ellint_3</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">k</span><span class="special">,</span> <span class="keyword">double</span> <span class="identifier">nu</span><span class="special">,</span> <span class="keyword">double</span> <span class="identifier">phi</span><span class="special">);</span> | |
358 | <span class="keyword">float</span> <span class="identifier">ellint_3f</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">k</span><span class="special">,</span> <span class="keyword">float</span> <span class="identifier">nu</span><span class="special">,</span> <span class="keyword">float</span> <span class="identifier">phi</span><span class="special">);</span> | |
359 | <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">ellint_3l</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">k</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">nu</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">phi</span><span class="special">);</span> | |
360 | </pre> | |
361 | <p> | |
362 | Returns the incomplete elliptic integral of the third kind of <span class="emphasis"><em>k</em></span>, | |
363 | <span class="emphasis"><em>nu</em></span> and <span class="emphasis"><em>phi</em></span>: | |
364 | </p> | |
365 | <p> | |
366 | <span class="inlinemediaobject"><img src="../../equations/ellint4.svg"></span> | |
367 | </p> | |
368 | <p> | |
369 | See also <a class="link" href="ellint/ellint_3.html" title="Elliptic Integrals of the Third Kind - Legendre Form">ellint_3</a> for the | |
370 | full template (header only) version of this function. | |
371 | </p> | |
372 | <pre class="programlisting"><span class="comment">// [5.2.1.15] exponential integral:</span> | |
373 | <span class="keyword">double</span> <span class="identifier">expint</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span> | |
374 | <span class="keyword">float</span> <span class="identifier">expintf</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">x</span><span class="special">);</span> | |
375 | <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">expintl</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span> | |
376 | </pre> | |
377 | <p> | |
378 | Returns the exponential integral Ei of <span class="emphasis"><em>x</em></span>: | |
379 | </p> | |
380 | <p> | |
381 | <span class="inlinemediaobject"><img src="../../equations/expint_i_1.svg"></span> | |
382 | </p> | |
383 | <p> | |
384 | See also <a class="link" href="expint/expint_i.html" title="Exponential Integral Ei">expint</a> for the | |
385 | full template (header only) version of this function. | |
386 | </p> | |
387 | <pre class="programlisting"><span class="comment">// [5.2.1.16] Hermite polynomials:</span> | |
388 | <span class="keyword">double</span> <span class="identifier">hermite</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">n</span><span class="special">,</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span> | |
389 | <span class="keyword">float</span> <span class="identifier">hermitef</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">n</span><span class="special">,</span> <span class="keyword">float</span> <span class="identifier">x</span><span class="special">);</span> | |
390 | <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">hermitel</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">n</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span> | |
391 | </pre> | |
392 | <p> | |
393 | Returns the n'th Hermite polynomial of <span class="emphasis"><em>x</em></span>: | |
394 | </p> | |
395 | <p> | |
396 | <span class="inlinemediaobject"><img src="../../equations/hermite_0.svg"></span> | |
397 | </p> | |
398 | <p> | |
399 | See also <a class="link" href="sf_poly/hermite.html" title="Hermite Polynomials">hermite</a> for the | |
400 | full template (header only) version of this function. | |
401 | </p> | |
402 | <pre class="programlisting"><span class="comment">// [5.2.1.18] Laguerre polynomials:</span> | |
403 | <span class="keyword">double</span> <span class="identifier">laguerre</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">n</span><span class="special">,</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span> | |
404 | <span class="keyword">float</span> <span class="identifier">laguerref</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">n</span><span class="special">,</span> <span class="keyword">float</span> <span class="identifier">x</span><span class="special">);</span> | |
405 | <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">laguerrel</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">n</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span> | |
406 | </pre> | |
407 | <p> | |
408 | Returns the n'th Laguerre polynomial of <span class="emphasis"><em>x</em></span>: | |
409 | </p> | |
410 | <p> | |
411 | <span class="inlinemediaobject"><img src="../../equations/laguerre_0.svg"></span> | |
412 | </p> | |
413 | <p> | |
414 | See also <a class="link" href="sf_poly/laguerre.html" title="Laguerre (and Associated) Polynomials">laguerre</a> for | |
415 | the full template (header only) version of this function. | |
416 | </p> | |
417 | <pre class="programlisting"><span class="comment">// [5.2.1.19] Legendre polynomials:</span> | |
418 | <span class="keyword">double</span> <span class="identifier">legendre</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">l</span><span class="special">,</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span> | |
419 | <span class="keyword">float</span> <span class="identifier">legendref</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">l</span><span class="special">,</span> <span class="keyword">float</span> <span class="identifier">x</span><span class="special">);</span> | |
420 | <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">legendrel</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">l</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span> | |
421 | </pre> | |
422 | <p> | |
423 | Returns the l'th Legendre polynomial of <span class="emphasis"><em>x</em></span>: | |
424 | </p> | |
425 | <p> | |
426 | <span class="inlinemediaobject"><img src="../../equations/legendre_0.svg"></span> | |
427 | </p> | |
428 | <p> | |
429 | See also <a class="link" href="sf_poly/legendre.html" title="Legendre (and Associated) Polynomials">legendre_p</a> for | |
430 | the full template (header only) version of this function. | |
431 | </p> | |
432 | <pre class="programlisting"><span class="comment">// [5.2.1.20] Riemann zeta function:</span> | |
433 | <span class="keyword">double</span> <span class="identifier">riemann_zeta</span><span class="special">(</span><span class="keyword">double</span><span class="special">);</span> | |
434 | <span class="keyword">float</span> <span class="identifier">riemann_zetaf</span><span class="special">(</span><span class="keyword">float</span><span class="special">);</span> | |
435 | <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">riemann_zetal</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">);</span> | |
436 | </pre> | |
437 | <p> | |
438 | Returns the Riemann Zeta function of <span class="emphasis"><em>x</em></span>: | |
439 | </p> | |
440 | <p> | |
441 | <span class="inlinemediaobject"><img src="../../equations/zeta1.svg"></span> | |
442 | </p> | |
443 | <p> | |
444 | See also <a class="link" href="zetas/zeta.html" title="Riemann Zeta Function">zeta</a> for the full template | |
445 | (header only) version of this function. | |
446 | </p> | |
447 | <pre class="programlisting"><span class="comment">// [5.2.1.21] spherical Bessel functions (of the first kind):</span> | |
448 | <span class="keyword">double</span> <span class="identifier">sph_bessel</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">n</span><span class="special">,</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span> | |
449 | <span class="keyword">float</span> <span class="identifier">sph_besself</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">n</span><span class="special">,</span> <span class="keyword">float</span> <span class="identifier">x</span><span class="special">);</span> | |
450 | <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">sph_bessell</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">n</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span> | |
451 | </pre> | |
452 | <p> | |
453 | Returns the spherical Bessel function of the first kind of <span class="emphasis"><em>x</em></span> | |
454 | j<sub>n</sub>(x): | |
455 | </p> | |
456 | <p> | |
457 | <span class="inlinemediaobject"><img src="../../equations/sbessel2.svg"></span> | |
458 | </p> | |
459 | <p> | |
460 | See also <a class="link" href="bessel/sph_bessel.html" title="Spherical Bessel Functions of the First and Second Kinds">sph_bessel</a> for | |
461 | the full template (header only) version of this function. | |
462 | </p> | |
463 | <pre class="programlisting"><span class="comment">// [5.2.1.22] spherical associated Legendre functions:</span> | |
464 | <span class="keyword">double</span> <span class="identifier">sph_legendre</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">l</span><span class="special">,</span> <span class="keyword">unsigned</span> <span class="identifier">m</span><span class="special">,</span> <span class="keyword">double</span> <span class="identifier">theta</span><span class="special">);</span> | |
465 | <span class="keyword">float</span> <span class="identifier">sph_legendref</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">l</span><span class="special">,</span> <span class="keyword">unsigned</span> <span class="identifier">m</span><span class="special">,</span> <span class="keyword">float</span> <span class="identifier">theta</span><span class="special">);</span> | |
466 | <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">sph_legendrel</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">l</span><span class="special">,</span> <span class="keyword">unsigned</span> <span class="identifier">m</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">theta</span><span class="special">);</span> | |
467 | </pre> | |
468 | <p> | |
469 | Returns the spherical associated Legendre function of <span class="emphasis"><em>l</em></span>, | |
470 | <span class="emphasis"><em>m</em></span> and <span class="emphasis"><em>theta</em></span>: | |
471 | </p> | |
472 | <p> | |
473 | <span class="inlinemediaobject"><img src="../../equations/spherical_3.svg"></span> | |
474 | </p> | |
475 | <p> | |
476 | See also <a class="link" href="sf_poly/sph_harm.html" title="Spherical Harmonics">spherical_harmonic</a> | |
477 | for the full template (header only) version of this function. | |
478 | </p> | |
479 | <pre class="programlisting"><span class="comment">// [5.2.1.23] spherical Neumann functions;</span> | |
480 | <span class="comment">// spherical Bessel functions (of the second kind):</span> | |
481 | <span class="keyword">double</span> <span class="identifier">sph_neumann</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">n</span><span class="special">,</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span> | |
482 | <span class="keyword">float</span> <span class="identifier">sph_neumannf</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">n</span><span class="special">,</span> <span class="keyword">float</span> <span class="identifier">x</span><span class="special">);</span> | |
483 | <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">sph_neumannl</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">n</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span> | |
484 | </pre> | |
485 | <p> | |
486 | Returns the spherical Neumann function of <span class="emphasis"><em>x</em></span> y<sub>n</sub>(x): | |
487 | </p> | |
488 | <p> | |
489 | <span class="inlinemediaobject"><img src="../../equations/sbessel2.svg"></span> | |
490 | </p> | |
491 | <p> | |
492 | See also <a class="link" href="bessel/sph_bessel.html" title="Spherical Bessel Functions of the First and Second Kinds">sph_bessel</a> for | |
493 | the full template (header only) version of this function. | |
494 | </p> | |
495 | <h5> | |
496 | <a name="math_toolkit.tr1_ref.h2"></a> | |
497 | <span class="phrase"><a name="math_toolkit.tr1_ref.currently_unsupported_tr1_functi"></a></span><a class="link" href="tr1_ref.html#math_toolkit.tr1_ref.currently_unsupported_tr1_functi">Currently | |
498 | Unsupported TR1 Functions</a> | |
499 | </h5> | |
500 | <pre class="programlisting"><span class="comment">// [5.2.1.7] confluent hypergeometric functions:</span> | |
501 | <span class="keyword">double</span> <span class="identifier">conf_hyperg</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">a</span><span class="special">,</span> <span class="keyword">double</span> <span class="identifier">c</span><span class="special">,</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span> | |
502 | <span class="keyword">float</span> <span class="identifier">conf_hypergf</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">a</span><span class="special">,</span> <span class="keyword">float</span> <span class="identifier">c</span><span class="special">,</span> <span class="keyword">float</span> <span class="identifier">x</span><span class="special">);</span> | |
503 | <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">conf_hypergl</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">a</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">c</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span> | |
504 | ||
505 | <span class="comment">// [5.2.1.17] hypergeometric functions:</span> | |
506 | <span class="keyword">double</span> <span class="identifier">hyperg</span><span class="special">(</span><span class="keyword">double</span> <span class="identifier">a</span><span class="special">,</span> <span class="keyword">double</span> <span class="identifier">b</span><span class="special">,</span> <span class="keyword">double</span> <span class="identifier">c</span><span class="special">,</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span> | |
507 | <span class="keyword">float</span> <span class="identifier">hypergf</span><span class="special">(</span><span class="keyword">float</span> <span class="identifier">a</span><span class="special">,</span> <span class="keyword">float</span> <span class="identifier">b</span><span class="special">,</span> <span class="keyword">float</span> <span class="identifier">c</span><span class="special">,</span> <span class="keyword">float</span> <span class="identifier">x</span><span class="special">);</span> | |
508 | <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">hypergl</span><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">a</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">b</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">c</span><span class="special">,</span> | |
509 | <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">x</span><span class="special">);</span> | |
510 | </pre> | |
511 | <div class="note"><table border="0" summary="Note"> | |
512 | <tr> | |
513 | <td rowspan="2" align="center" valign="top" width="25"><img alt="[Note]" src="../../../../../doc/src/images/note.png"></td> | |
514 | <th align="left">Note</th> | |
515 | </tr> | |
516 | <tr><td align="left" valign="top"><p> | |
517 | These two functions are not implemented as they are not believed to be numerically | |
518 | stable. | |
519 | </p></td></tr> | |
520 | </table></div> | |
521 | </div> | |
522 | <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> | |
523 | <td align="left"></td> | |
524 | <td align="right"><div class="copyright-footer">Copyright © 2006-2010, 2012-2014 Nikhar Agrawal, | |
525 | Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert | |
526 | Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan Råde, Gautam Sewani, | |
527 | Benjamin Sobotta, Thijs van den Berg, Daryle Walker and Xiaogang Zhang<p> | |
528 | Distributed under the Boost Software License, Version 1.0. (See accompanying | |
529 | file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) | |
530 | </p> | |
531 | </div></td> | |
532 | </tr></table> | |
533 | <hr> | |
534 | <div class="spirit-nav"> | |
535 | <a accesskey="p" href="c99.html"><img src="../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../extern_c.html"><img src="../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="../inverse_complex.html"><img src="../../../../../doc/src/images/next.png" alt="Next"></a> | |
536 | </div> | |
537 | </body> | |
538 | </html> |