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 Special Functions
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26 <div class=
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27 <a name=
"special"></a>Chapter
 6.
 Special Functions
</h1></div></div></div>
29 <p><b>Table of Contents
</b></p>
31 <dt><span class=
"section"><a href=
"math_toolkit/number_series.html">Number Series
</a></span></dt>
33 <dt><span class=
"section"><a href=
"math_toolkit/number_series/bernoulli_numbers.html">Bernoulli
34 Numbers
</a></span></dt>
35 <dt><span class=
"section"><a href=
"math_toolkit/number_series/tangent_numbers.html">Tangent Numbers
</a></span></dt>
36 <dt><span class=
"section"><a href=
"math_toolkit/number_series/primes.html">Prime Numbers
</a></span></dt>
38 <dt><span class=
"section"><a href=
"math_toolkit/sf_gamma.html">Gamma Functions
</a></span></dt>
40 <dt><span class=
"section"><a href=
"math_toolkit/sf_gamma/tgamma.html">Gamma
</a></span></dt>
41 <dt><span class=
"section"><a href=
"math_toolkit/sf_gamma/lgamma.html">Log Gamma
</a></span></dt>
42 <dt><span class=
"section"><a href=
"math_toolkit/sf_gamma/digamma.html">Digamma
</a></span></dt>
43 <dt><span class=
"section"><a href=
"math_toolkit/sf_gamma/trigamma.html">Trigamma
</a></span></dt>
44 <dt><span class=
"section"><a href=
"math_toolkit/sf_gamma/polygamma.html">Polygamma
</a></span></dt>
45 <dt><span class=
"section"><a href=
"math_toolkit/sf_gamma/gamma_ratios.html">Ratios of Gamma Functions
</a></span></dt>
46 <dt><span class=
"section"><a href=
"math_toolkit/sf_gamma/igamma.html">Incomplete Gamma Functions
</a></span></dt>
47 <dt><span class=
"section"><a href=
"math_toolkit/sf_gamma/igamma_inv.html">Incomplete Gamma Function
48 Inverses
</a></span></dt>
49 <dt><span class=
"section"><a href=
"math_toolkit/sf_gamma/gamma_derivatives.html">Derivative of
50 the Incomplete Gamma Function
</a></span></dt>
52 <dt><span class=
"section"><a href=
"math_toolkit/factorials.html">Factorials and Binomial Coefficients
</a></span></dt>
54 <dt><span class=
"section"><a href=
"math_toolkit/factorials/sf_factorial.html">Factorial
</a></span></dt>
55 <dt><span class=
"section"><a href=
"math_toolkit/factorials/sf_double_factorial.html">Double Factorial
</a></span></dt>
56 <dt><span class=
"section"><a href=
"math_toolkit/factorials/sf_rising_factorial.html">Rising Factorial
</a></span></dt>
57 <dt><span class=
"section"><a href=
"math_toolkit/factorials/sf_falling_factorial.html">Falling
58 Factorial
</a></span></dt>
59 <dt><span class=
"section"><a href=
"math_toolkit/factorials/sf_binomial.html">Binomial Coefficients
</a></span></dt>
61 <dt><span class=
"section"><a href=
"math_toolkit/sf_beta.html">Beta Functions
</a></span></dt>
63 <dt><span class=
"section"><a href=
"math_toolkit/sf_beta/beta_function.html">Beta
</a></span></dt>
64 <dt><span class=
"section"><a href=
"math_toolkit/sf_beta/ibeta_function.html">Incomplete Beta
65 Functions
</a></span></dt>
66 <dt><span class=
"section"><a href=
"math_toolkit/sf_beta/ibeta_inv_function.html">The Incomplete
67 Beta Function Inverses
</a></span></dt>
68 <dt><span class=
"section"><a href=
"math_toolkit/sf_beta/beta_derivative.html">Derivative of the
69 Incomplete Beta Function
</a></span></dt>
71 <dt><span class=
"section"><a href=
"math_toolkit/sf_erf.html">Error Functions
</a></span></dt>
73 <dt><span class=
"section"><a href=
"math_toolkit/sf_erf/error_function.html">Error Functions
</a></span></dt>
74 <dt><span class=
"section"><a href=
"math_toolkit/sf_erf/error_inv.html">Error Function Inverses
</a></span></dt>
76 <dt><span class=
"section"><a href=
"math_toolkit/sf_poly.html">Polynomials
</a></span></dt>
78 <dt><span class=
"section"><a href=
"math_toolkit/sf_poly/legendre.html">Legendre (and Associated)
79 Polynomials
</a></span></dt>
80 <dt><span class=
"section"><a href=
"math_toolkit/sf_poly/laguerre.html">Laguerre (and Associated)
81 Polynomials
</a></span></dt>
82 <dt><span class=
"section"><a href=
"math_toolkit/sf_poly/hermite.html">Hermite Polynomials
</a></span></dt>
83 <dt><span class=
"section"><a href=
"math_toolkit/sf_poly/sph_harm.html">Spherical Harmonics
</a></span></dt>
85 <dt><span class=
"section"><a href=
"math_toolkit/bessel.html">Bessel Functions
</a></span></dt>
87 <dt><span class=
"section"><a href=
"math_toolkit/bessel/bessel_over.html">Bessel Function Overview
</a></span></dt>
88 <dt><span class=
"section"><a href=
"math_toolkit/bessel/bessel_first.html">Bessel Functions of
89 the First and Second Kinds
</a></span></dt>
90 <dt><span class=
"section"><a href=
"math_toolkit/bessel/bessel_root.html">Finding Zeros of Bessel
91 Functions of the First and Second Kinds
</a></span></dt>
92 <dt><span class=
"section"><a href=
"math_toolkit/bessel/mbessel.html">Modified Bessel Functions
93 of the First and Second Kinds
</a></span></dt>
94 <dt><span class=
"section"><a href=
"math_toolkit/bessel/sph_bessel.html">Spherical Bessel Functions
95 of the First and Second Kinds
</a></span></dt>
96 <dt><span class=
"section"><a href=
"math_toolkit/bessel/bessel_derivatives.html">Derivatives of
97 the Bessel Functions
</a></span></dt>
99 <dt><span class=
"section"><a href=
"math_toolkit/hankel.html">Hankel Functions
</a></span></dt>
101 <dt><span class=
"section"><a href=
"math_toolkit/hankel/cyl_hankel.html">Cyclic Hankel Functions
</a></span></dt>
102 <dt><span class=
"section"><a href=
"math_toolkit/hankel/sph_hankel.html">Spherical Hankel Functions
</a></span></dt>
104 <dt><span class=
"section"><a href=
"math_toolkit/airy.html">Airy Functions
</a></span></dt>
106 <dt><span class=
"section"><a href=
"math_toolkit/airy/ai.html">Airy Ai Function
</a></span></dt>
107 <dt><span class=
"section"><a href=
"math_toolkit/airy/bi.html">Airy Bi Function
</a></span></dt>
108 <dt><span class=
"section"><a href=
"math_toolkit/airy/aip.html">Airy Ai' Function
</a></span></dt>
109 <dt><span class=
"section"><a href=
"math_toolkit/airy/bip.html">Airy Bi' Function
</a></span></dt>
110 <dt><span class=
"section"><a href=
"math_toolkit/airy/airy_root.html">Finding Zeros of Airy Functions
</a></span></dt>
112 <dt><span class=
"section"><a href=
"math_toolkit/ellint.html">Elliptic Integrals
</a></span></dt>
114 <dt><span class=
"section"><a href=
"math_toolkit/ellint/ellint_intro.html">Elliptic Integral Overview
</a></span></dt>
115 <dt><span class=
"section"><a href=
"math_toolkit/ellint/ellint_carlson.html">Elliptic Integrals
116 - Carlson Form
</a></span></dt>
117 <dt><span class=
"section"><a href=
"math_toolkit/ellint/ellint_1.html">Elliptic Integrals of the
118 First Kind - Legendre Form
</a></span></dt>
119 <dt><span class=
"section"><a href=
"math_toolkit/ellint/ellint_2.html">Elliptic Integrals of the
120 Second Kind - Legendre Form
</a></span></dt>
121 <dt><span class=
"section"><a href=
"math_toolkit/ellint/ellint_3.html">Elliptic Integrals of the
122 Third Kind - Legendre Form
</a></span></dt>
123 <dt><span class=
"section"><a href=
"math_toolkit/ellint/ellint_d.html">Elliptic Integral D - Legendre
125 <dt><span class=
"section"><a href=
"math_toolkit/ellint/jacobi_zeta.html">Jacobi Zeta Function
</a></span></dt>
126 <dt><span class=
"section"><a href=
"math_toolkit/ellint/heuman_lambda.html">Heuman Lambda Function
</a></span></dt>
128 <dt><span class=
"section"><a href=
"math_toolkit/jacobi.html">Jacobi Elliptic Functions
</a></span></dt>
130 <dt><span class=
"section"><a href=
"math_toolkit/jacobi/jac_over.html">Overvew of the Jacobi Elliptic
131 Functions
</a></span></dt>
132 <dt><span class=
"section"><a href=
"math_toolkit/jacobi/jacobi_elliptic.html">Jacobi Elliptic
133 SN, CN and DN
</a></span></dt>
134 <dt><span class=
"section"><a href=
"math_toolkit/jacobi/jacobi_cd.html">Jacobi Elliptic Function
136 <dt><span class=
"section"><a href=
"math_toolkit/jacobi/jacobi_cn.html">Jacobi Elliptic Function
138 <dt><span class=
"section"><a href=
"math_toolkit/jacobi/jacobi_cs.html">Jacobi Elliptic Function
140 <dt><span class=
"section"><a href=
"math_toolkit/jacobi/jacobi_dc.html">Jacobi Elliptic Function
142 <dt><span class=
"section"><a href=
"math_toolkit/jacobi/jacobi_dn.html">Jacobi Elliptic Function
144 <dt><span class=
"section"><a href=
"math_toolkit/jacobi/jacobi_ds.html">Jacobi Elliptic Function
146 <dt><span class=
"section"><a href=
"math_toolkit/jacobi/jacobi_nc.html">Jacobi Elliptic Function
148 <dt><span class=
"section"><a href=
"math_toolkit/jacobi/jacobi_nd.html">Jacobi Elliptic Function
150 <dt><span class=
"section"><a href=
"math_toolkit/jacobi/jacobi_ns.html">Jacobi Elliptic Function
152 <dt><span class=
"section"><a href=
"math_toolkit/jacobi/jacobi_sc.html">Jacobi Elliptic Function
154 <dt><span class=
"section"><a href=
"math_toolkit/jacobi/jacobi_sd.html">Jacobi Elliptic Function
156 <dt><span class=
"section"><a href=
"math_toolkit/jacobi/jacobi_sn.html">Jacobi Elliptic Function
159 <dt><span class=
"section"><a href=
"math_toolkit/zetas.html">Zeta Functions
</a></span></dt>
160 <dd><dl><dt><span class=
"section"><a href=
"math_toolkit/zetas/zeta.html">Riemann Zeta Function
</a></span></dt></dl></dd>
161 <dt><span class=
"section"><a href=
"math_toolkit/expint.html">Exponential Integrals
</a></span></dt>
163 <dt><span class=
"section"><a href=
"math_toolkit/expint/expint_n.html">Exponential Integral En
</a></span></dt>
164 <dt><span class=
"section"><a href=
"math_toolkit/expint/expint_i.html">Exponential Integral Ei
</a></span></dt>
166 <dt><span class=
"section"><a href=
"math_toolkit/powers.html">Basic Functions
</a></span></dt>
168 <dt><span class=
"section"><a href=
"math_toolkit/powers/sin_pi.html">sin_pi
</a></span></dt>
169 <dt><span class=
"section"><a href=
"math_toolkit/powers/cos_pi.html">cos_pi
</a></span></dt>
170 <dt><span class=
"section"><a href=
"math_toolkit/powers/log1p.html">log1p
</a></span></dt>
171 <dt><span class=
"section"><a href=
"math_toolkit/powers/expm1.html">expm1
</a></span></dt>
172 <dt><span class=
"section"><a href=
"math_toolkit/powers/cbrt.html">cbrt
</a></span></dt>
173 <dt><span class=
"section"><a href=
"math_toolkit/powers/sqrt1pm1.html">sqrt1pm1
</a></span></dt>
174 <dt><span class=
"section"><a href=
"math_toolkit/powers/powm1.html">powm1
</a></span></dt>
175 <dt><span class=
"section"><a href=
"math_toolkit/powers/hypot.html">hypot
</a></span></dt>
176 <dt><span class=
"section"><a href=
"math_toolkit/powers/ct_pow.html">Compile Time Power of a Runtime
179 <dt><span class=
"section"><a href=
"math_toolkit/sinc.html">Sinus Cardinal and Hyperbolic Sinus
180 Cardinal Functions
</a></span></dt>
182 <dt><span class=
"section"><a href=
"math_toolkit/sinc/sinc_overview.html">Sinus Cardinal and Hyperbolic
183 Sinus Cardinal Functions Overview
</a></span></dt>
184 <dt><span class=
"section"><a href=
"math_toolkit/sinc/sinc_pi.html">sinc_pi
</a></span></dt>
185 <dt><span class=
"section"><a href=
"math_toolkit/sinc/sinhc_pi.html">sinhc_pi
</a></span></dt>
187 <dt><span class=
"section"><a href=
"math_toolkit/inv_hyper.html">Inverse Hyperbolic Functions
</a></span></dt>
189 <dt><span class=
"section"><a href=
"math_toolkit/inv_hyper/inv_hyper_over.html">Inverse Hyperbolic
190 Functions Overview
</a></span></dt>
191 <dt><span class=
"section"><a href=
"math_toolkit/inv_hyper/acosh.html">acosh
</a></span></dt>
192 <dt><span class=
"section"><a href=
"math_toolkit/inv_hyper/asinh.html">asinh
</a></span></dt>
193 <dt><span class=
"section"><a href=
"math_toolkit/inv_hyper/atanh.html">atanh
</a></span></dt>
195 <dt><span class=
"section"><a href=
"math_toolkit/owens_t.html">Owen's T function
</a></span></dt>
199 <table xmlns:
rev=
"http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width=
"100%"><tr>
200 <td align=
"left"></td>
201 <td align=
"right"><div class=
"copyright-footer">Copyright
© 2006-
2010,
2012-
2014 Nikhar Agrawal,
202 Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert
203 Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R
åde, Gautam Sewani,
204 Benjamin Sobotta, Thijs van den Berg, Daryle Walker and Xiaogang Zhang
<p>
205 Distributed under the Boost Software License, Version
1.0. (See accompanying
206 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>)
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