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| 4 | <title>Chapter 6. Special Functions</title> | |
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| 24 | </div> | |
| 25 | <div class="chapter"> | |
| 26 | <div class="titlepage"><div><div><h1 class="title"> | |
| 27 | <a name="special"></a>Chapter 6. Special Functions</h1></div></div></div> | |
| 28 | <div class="toc"> | |
| 29 | <p><b>Table of Contents</b></p> | |
| 30 | <dl> | |
| 31 | <dt><span class="section"><a href="math_toolkit/number_series.html">Number Series</a></span></dt> | |
| 32 | <dd><dl> | |
| 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> | |
| 37 | </dl></dd> | |
| 38 | <dt><span class="section"><a href="math_toolkit/sf_gamma.html">Gamma Functions</a></span></dt> | |
| 39 | <dd><dl> | |
| 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> | |
| 51 | </dl></dd> | |
| 52 | <dt><span class="section"><a href="math_toolkit/factorials.html">Factorials and Binomial Coefficients</a></span></dt> | |
| 53 | <dd><dl> | |
| 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> | |
| 60 | </dl></dd> | |
| 61 | <dt><span class="section"><a href="math_toolkit/sf_beta.html">Beta Functions</a></span></dt> | |
| 62 | <dd><dl> | |
| 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> | |
| 70 | </dl></dd> | |
| 71 | <dt><span class="section"><a href="math_toolkit/sf_erf.html">Error Functions</a></span></dt> | |
| 72 | <dd><dl> | |
| 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> | |
| 75 | </dl></dd> | |
| 76 | <dt><span class="section"><a href="math_toolkit/sf_poly.html">Polynomials</a></span></dt> | |
| 77 | <dd><dl> | |
| 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> | |
| 84 | </dl></dd> | |
| 85 | <dt><span class="section"><a href="math_toolkit/bessel.html">Bessel Functions</a></span></dt> | |
| 86 | <dd><dl> | |
| 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> | |
| 98 | </dl></dd> | |
| 99 | <dt><span class="section"><a href="math_toolkit/hankel.html">Hankel Functions</a></span></dt> | |
| 100 | <dd><dl> | |
| 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> | |
| 103 | </dl></dd> | |
| 104 | <dt><span class="section"><a href="math_toolkit/airy.html">Airy Functions</a></span></dt> | |
| 105 | <dd><dl> | |
| 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> | |
| 111 | </dl></dd> | |
| 112 | <dt><span class="section"><a href="math_toolkit/ellint.html">Elliptic Integrals</a></span></dt> | |
| 113 | <dd><dl> | |
| 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 | |
| 124 | Form</a></span></dt> | |
| 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> | |
| 127 | </dl></dd> | |
| 128 | <dt><span class="section"><a href="math_toolkit/jacobi.html">Jacobi Elliptic Functions</a></span></dt> | |
| 129 | <dd><dl> | |
| 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 | |
| 135 | cd</a></span></dt> | |
| 136 | <dt><span class="section"><a href="math_toolkit/jacobi/jacobi_cn.html">Jacobi Elliptic Function | |
| 137 | cn</a></span></dt> | |
| 138 | <dt><span class="section"><a href="math_toolkit/jacobi/jacobi_cs.html">Jacobi Elliptic Function | |
| 139 | cs</a></span></dt> | |
| 140 | <dt><span class="section"><a href="math_toolkit/jacobi/jacobi_dc.html">Jacobi Elliptic Function | |
| 141 | dc</a></span></dt> | |
| 142 | <dt><span class="section"><a href="math_toolkit/jacobi/jacobi_dn.html">Jacobi Elliptic Function | |
| 143 | dn</a></span></dt> | |
| 144 | <dt><span class="section"><a href="math_toolkit/jacobi/jacobi_ds.html">Jacobi Elliptic Function | |
| 145 | ds</a></span></dt> | |
| 146 | <dt><span class="section"><a href="math_toolkit/jacobi/jacobi_nc.html">Jacobi Elliptic Function | |
| 147 | nc</a></span></dt> | |
| 148 | <dt><span class="section"><a href="math_toolkit/jacobi/jacobi_nd.html">Jacobi Elliptic Function | |
| 149 | nd</a></span></dt> | |
| 150 | <dt><span class="section"><a href="math_toolkit/jacobi/jacobi_ns.html">Jacobi Elliptic Function | |
| 151 | ns</a></span></dt> | |
| 152 | <dt><span class="section"><a href="math_toolkit/jacobi/jacobi_sc.html">Jacobi Elliptic Function | |
| 153 | sc</a></span></dt> | |
| 154 | <dt><span class="section"><a href="math_toolkit/jacobi/jacobi_sd.html">Jacobi Elliptic Function | |
| 155 | sd</a></span></dt> | |
| 156 | <dt><span class="section"><a href="math_toolkit/jacobi/jacobi_sn.html">Jacobi Elliptic Function | |
| 157 | sn</a></span></dt> | |
| 158 | </dl></dd> | |
| 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> | |
| 162 | <dd><dl> | |
| 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> | |
| 165 | </dl></dd> | |
| 166 | <dt><span class="section"><a href="math_toolkit/powers.html">Basic Functions</a></span></dt> | |
| 167 | <dd><dl> | |
| 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 | |
| 177 | Base</a></span></dt> | |
| 178 | </dl></dd> | |
| 179 | <dt><span class="section"><a href="math_toolkit/sinc.html">Sinus Cardinal and Hyperbolic Sinus | |
| 180 | Cardinal Functions</a></span></dt> | |
| 181 | <dd><dl> | |
| 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> | |
| 186 | </dl></dd> | |
| 187 | <dt><span class="section"><a href="math_toolkit/inv_hyper.html">Inverse Hyperbolic Functions</a></span></dt> | |
| 188 | <dd><dl> | |
| 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> | |
| 194 | </dl></dd> | |
| 195 | <dt><span class="section"><a href="math_toolkit/owens_t.html">Owen's T function</a></span></dt> | |
| 196 | </dl> | |
| 197 | </div> | |
| 198 | </div> | |
| 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 Råde, 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>) | |
| 207 | </p> | |
| 208 | </div></td> | |
| 209 | </tr></table> | |
| 210 | <hr> | |
| 211 | <div class="spirit-nav"> | |
| 212 | <a accesskey="p" href="math_toolkit/future.html"><img src="../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="index.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="math_toolkit/number_series.html"><img src="../../../../doc/src/images/next.png" alt="Next"></a> | |
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