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30 <a name=
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31 <span class=
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"tr1_ref.html#math_toolkit.tr1_ref.supported_tr1_functions">Supported
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>
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>
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>
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>
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>
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>
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>
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>
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>
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>
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>
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>
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>
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>
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>
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>
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>
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>
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>
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>
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>
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>
143 <span class=
"special">}}}}
</span> <span class=
"comment">// namespaces
</span>
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>.
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>
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
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>
174 The assoc_laguerre functions return:
177 <span class=
"inlinemediaobject"><img src=
"../../equations/laguerre_1.svg"></span>
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.
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>
189 The assoc_legendre functions return:
192 <span class=
"inlinemediaobject"><img src=
"../../equations/legendre_1b.svg"></span>
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.
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>
204 Returns the beta function of
<span class=
"emphasis"><em>x
</em></span> and
<span class=
"emphasis"><em>y
</em></span>:
207 <span class=
"inlinemediaobject"><img src=
"../../equations/beta1.svg"></span>
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.
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>
219 Returns the complete elliptic integral of the first kind of
<span class=
"emphasis"><em>k
</em></span>:
222 <span class=
"inlinemediaobject"><img src=
"../../equations/ellint6.svg"></span>
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.
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>
234 Returns the complete elliptic integral of the second kind of
<span class=
"emphasis"><em>k
</em></span>:
237 <span class=
"inlinemediaobject"><img src=
"../../equations/ellint7.svg"></span>
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.
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>
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>:
253 <span class=
"inlinemediaobject"><img src=
"../../equations/ellint8.svg"></span>
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.
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>
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>:
269 <span class=
"inlinemediaobject"><img src=
"../../equations/mbessel2.svg"></span>
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.
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>
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>:
285 <span class=
"inlinemediaobject"><img src=
"../../equations/bessel2.svg"></span>
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.
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>
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>:
301 <span class=
"inlinemediaobject"><img src=
"../../equations/mbessel3.svg"></span>
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.
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>
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>:
318 <span class=
"inlinemediaobject"><img src=
"../../equations/bessel3.svg"></span>
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.
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>
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>:
334 <span class=
"inlinemediaobject"><img src=
"../../equations/ellint2.svg"></span>
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.
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>
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>:
350 <span class=
"inlinemediaobject"><img src=
"../../equations/ellint3.svg"></span>
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.
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>
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>:
366 <span class=
"inlinemediaobject"><img src=
"../../equations/ellint4.svg"></span>
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.
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>
378 Returns the exponential integral Ei of
<span class=
"emphasis"><em>x
</em></span>:
381 <span class=
"inlinemediaobject"><img src=
"../../equations/expint_i_1.svg"></span>
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.
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>
393 Returns the n'th Hermite polynomial of
<span class=
"emphasis"><em>x
</em></span>:
396 <span class=
"inlinemediaobject"><img src=
"../../equations/hermite_0.svg"></span>
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.
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>
408 Returns the n'th Laguerre polynomial of
<span class=
"emphasis"><em>x
</em></span>:
411 <span class=
"inlinemediaobject"><img src=
"../../equations/laguerre_0.svg"></span>
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.
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>
423 Returns the l'th Legendre polynomial of
<span class=
"emphasis"><em>x
</em></span>:
426 <span class=
"inlinemediaobject"><img src=
"../../equations/legendre_0.svg"></span>
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.
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>
438 Returns the Riemann Zeta function of
<span class=
"emphasis"><em>x
</em></span>:
441 <span class=
"inlinemediaobject"><img src=
"../../equations/zeta1.svg"></span>
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.
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>
453 Returns the spherical Bessel function of the first kind of
<span class=
"emphasis"><em>x
</em></span>
457 <span class=
"inlinemediaobject"><img src=
"../../equations/sbessel2.svg"></span>
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.
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>
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>:
473 <span class=
"inlinemediaobject"><img src=
"../../equations/spherical_3.svg"></span>
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.
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>
486 Returns the spherical Neumann function of
<span class=
"emphasis"><em>x
</em></span> y
<sub>n
</sub>(x):
489 <span class=
"inlinemediaobject"><img src=
"../../equations/sbessel2.svg"></span>
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.
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>
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>
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>
511 <div class=
"note"><table border=
"0" summary=
"Note">
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>
516 <tr><td align=
"left" valign=
"top"><p>
517 These two functions are not implemented as they are not believed to be numerically
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 R
åde, 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>)
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=
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