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<html> <head> <meta http-equiv="Content-Type" content="text/html; charset=US-ASCII"> <title>Chapter 6. Special Functions</title> <link rel="stylesheet" href="math.css" type="text/css"> <meta name="generator" content="DocBook XSL Stylesheets V1.78.1"> <link rel="home" href="index.html" title="Math Toolkit 2.1.0"> <link rel="up" href="index.html" title="Math Toolkit 2.1.0"> <link rel="prev" href="math_toolkit/future.html" title="Extras/Future Directions"> <link rel="next" href="math_toolkit/number_series.html" title="Number Series"> </head> <body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF"> <table cellpadding="2" width="100%"><tr> <td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../boost.png"></td> <td align="center"><a href="../../../../index.html">Home</a></td> <td align="center"><a href="../../../../libs/libraries.htm">Libraries</a></td> <td align="center"><a 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href="math_toolkit/number_series/bernoulli_numbers.html">Bernoulli Numbers</a></dt> <dt><a href="math_toolkit/number_series/tangent_numbers.html">Tangent Numbers</a></dt> <dt><a href="math_toolkit/number_series/primes.html">Prime Numbers</a></dt> </dl></dd> <dt><a href="math_toolkit/sf_gamma.html">Gamma Functions</a></dt> <dd><dl> <dt><a href="math_toolkit/sf_gamma/tgamma.html">Gamma</a></dt> <dt><a href="math_toolkit/sf_gamma/lgamma.html">Log Gamma</a></dt> <dt><a href="math_toolkit/sf_gamma/digamma.html">Digamma</a></dt> <dt><a href="math_toolkit/sf_gamma/gamma_ratios.html">Ratios of Gamma Functions</a></dt> <dt><a href="math_toolkit/sf_gamma/igamma.html">Incomplete Gamma Functions</a></dt> <dt><a href="math_toolkit/sf_gamma/igamma_inv.html">Incomplete Gamma Function Inverses</a></dt> <dt><a href="math_toolkit/sf_gamma/gamma_derivatives.html">Derivative of the Incomplete Gamma Function</a></dt> </dl></dd> <dt><a href="math_toolkit/factorials.html">Factorials and Binomial Coefficients</a></dt> <dd><dl> <dt><a href="math_toolkit/factorials/sf_factorial.html">Factorial</a></dt> <dt><a href="math_toolkit/factorials/sf_double_factorial.html">Double Factorial</a></dt> <dt><a href="math_toolkit/factorials/sf_rising_factorial.html">Rising Factorial</a></dt> <dt><a href="math_toolkit/factorials/sf_falling_factorial.html">Falling Factorial</a></dt> <dt><a href="math_toolkit/factorials/sf_binomial.html">Binomial Coefficients</a></dt> </dl></dd> <dt><a href="math_toolkit/sf_beta.html">Beta Functions</a></dt> <dd><dl> <dt><a href="math_toolkit/sf_beta/beta_function.html">Beta</a></dt> <dt><a href="math_toolkit/sf_beta/ibeta_function.html">Incomplete Beta Functions</a></dt> <dt><a href="math_toolkit/sf_beta/ibeta_inv_function.html">The Incomplete Beta Function Inverses</a></dt> <dt><a href="math_toolkit/sf_beta/beta_derivative.html">Derivative of the Incomplete Beta Function</a></dt> </dl></dd> <dt><a href="math_toolkit/sf_erf.html">Error Functions</a></dt> <dd><dl> <dt><a href="math_toolkit/sf_erf/error_function.html">Error Functions</a></dt> <dt><a href="math_toolkit/sf_erf/error_inv.html">Error Function Inverses</a></dt> </dl></dd> <dt><a href="math_toolkit/sf_poly.html">Polynomials</a></dt> <dd><dl> <dt><a href="math_toolkit/sf_poly/legendre.html">Legendre (and Associated) Polynomials</a></dt> <dt><a href="math_toolkit/sf_poly/laguerre.html">Laguerre (and Associated) Polynomials</a></dt> <dt><a href="math_toolkit/sf_poly/hermite.html">Hermite Polynomials</a></dt> <dt><a href="math_toolkit/sf_poly/sph_harm.html">Spherical Harmonics</a></dt> </dl></dd> <dt><a href="math_toolkit/bessel.html">Bessel Functions</a></dt> <dd><dl> <dt><a href="math_toolkit/bessel/bessel_over.html">Bessel Function Overview</a></dt> <dt><a href="math_toolkit/bessel/bessel_first.html">Bessel Functions of the First and Second Kinds</a></dt> <dt><a href="math_toolkit/bessel/bessel_root.html">Finding Zeros of Bessel Functions of the First and Second Kinds</a></dt> <dt><a href="math_toolkit/bessel/mbessel.html">Modified Bessel Functions of the First and Second Kinds</a></dt> <dt><a href="math_toolkit/bessel/sph_bessel.html">Spherical Bessel Functions of the First and Second Kinds</a></dt> <dt><a href="math_toolkit/bessel/bessel_derivatives.html">Derivatives of the Bessel Functions</a></dt> </dl></dd> <dt><a href="math_toolkit/hankel.html">Hankel Functions</a></dt> <dd><dl> <dt><a href="math_toolkit/hankel/cyl_hankel.html">Cyclic Hankel Functions</a></dt> <dt><a href="math_toolkit/hankel/sph_hankel.html">Spherical Hankel Functions</a></dt> </dl></dd> <dt><a href="math_toolkit/airy.html">Airy Functions</a></dt> <dd><dl> <dt><a href="math_toolkit/airy/ai.html">Airy Ai Function</a></dt> <dt><a href="math_toolkit/airy/bi.html">Airy Bi Function</a></dt> <dt><a href="math_toolkit/airy/aip.html">Airy Ai' Function</a></dt> <dt><a href="math_toolkit/airy/bip.html">Airy Bi' Function</a></dt> </dl></dd> <dt><a href="math_toolkit/ellint.html">Elliptic Integrals</a></dt> <dd><dl> <dt><a href="math_toolkit/ellint/ellint_intro.html">Elliptic Integral Overview</a></dt> <dt><a href="math_toolkit/ellint/ellint_carlson.html">Elliptic Integrals - Carlson Form</a></dt> <dt><a href="math_toolkit/ellint/ellint_1.html">Elliptic Integrals of the First Kind - Legendre Form</a></dt> <dt><a href="math_toolkit/ellint/ellint_2.html">Elliptic Integrals of the Second Kind - Legendre Form</a></dt> <dt><a href="math_toolkit/ellint/ellint_3.html">Elliptic Integrals of the Third Kind - Legendre Form</a></dt> </dl></dd> <dt><a href="math_toolkit/jacobi.html">Jacobi Elliptic Functions</a></dt> <dd><dl> <dt><a href="math_toolkit/jacobi/jac_over.html">Overvew of the Jacobi Elliptic Functions</a></dt> <dt><a href="math_toolkit/jacobi/jacobi_elliptic.html">Jacobi Elliptic SN, CN and DN</a></dt> <dt><a href="math_toolkit/jacobi/jacobi_cd.html">Jacobi Elliptic Function cd</a></dt> <dt><a href="math_toolkit/jacobi/jacobi_cn.html">Jacobi Elliptic Function cn</a></dt> <dt><a href="math_toolkit/jacobi/jacobi_cs.html">Jacobi Elliptic Function cs</a></dt> <dt><a href="math_toolkit/jacobi/jacobi_dc.html">Jacobi Elliptic Function dc</a></dt> <dt><a href="math_toolkit/jacobi/jacobi_dn.html">Jacobi Elliptic Function dn</a></dt> <dt><a href="math_toolkit/jacobi/jacobi_ds.html">Jacobi Elliptic Function ds</a></dt> <dt><a href="math_toolkit/jacobi/jacobi_nc.html">Jacobi Elliptic Function nc</a></dt> <dt><a href="math_toolkit/jacobi/jacobi_nd.html">Jacobi Elliptic Function nd</a></dt> <dt><a href="math_toolkit/jacobi/jacobi_ns.html">Jacobi Elliptic Function ns</a></dt> <dt><a href="math_toolkit/jacobi/jacobi_sc.html">Jacobi Elliptic Function sc</a></dt> <dt><a href="math_toolkit/jacobi/jacobi_sd.html">Jacobi Elliptic Function sd</a></dt> <dt><a href="math_toolkit/jacobi/jacobi_sn.html">Jacobi Elliptic Function sn</a></dt> </dl></dd> <dt><a href="math_toolkit/zetas.html">Zeta Functions</a></dt> <dd><dl><dt><a href="math_toolkit/zetas/zeta.html">Riemann Zeta Function</a></dt></dl></dd> <dt><a href="math_toolkit/expint.html">Exponential Integrals</a></dt> <dd><dl> <dt><a href="math_toolkit/expint/expint_n.html">Exponential Integral En</a></dt> <dt><a href="math_toolkit/expint/expint_i.html">Exponential Integral Ei</a></dt> </dl></dd> <dt><a href="math_toolkit/powers.html">Basic Functions</a></dt> <dd><dl> <dt><a href="math_toolkit/powers/sin_pi.html">sin_pi</a></dt> <dt><a href="math_toolkit/powers/cos_pi.html">cos_pi</a></dt> <dt><a href="math_toolkit/powers/log1p.html">log1p</a></dt> <dt><a href="math_toolkit/powers/expm1.html">expm1</a></dt> <dt><a href="math_toolkit/powers/cbrt.html">cbrt</a></dt> <dt><a href="math_toolkit/powers/sqrt1pm1.html">sqrt1pm1</a></dt> <dt><a href="math_toolkit/powers/powm1.html">powm1</a></dt> <dt><a href="math_toolkit/powers/hypot.html">hypot</a></dt> <dt><a href="math_toolkit/powers/ct_pow.html">Compile Time Power of a Runtime Base</a></dt> </dl></dd> <dt><a href="math_toolkit/sinc.html">Sinus Cardinal and Hyperbolic Sinus Cardinal Functions</a></dt> <dd><dl> <dt><a href="math_toolkit/sinc/sinc_overview.html">Sinus Cardinal and Hyperbolic Sinus Cardinal Functions Overview</a></dt> <dt><a href="math_toolkit/sinc/sinc_pi.html">sinc_pi</a></dt> <dt><a href="math_toolkit/sinc/sinhc_pi.html">sinhc_pi</a></dt> </dl></dd> <dt><a href="math_toolkit/inv_hyper.html">Inverse Hyperbolic Functions</a></dt> <dd><dl> <dt><a href="math_toolkit/inv_hyper/inv_hyper_over.html">Inverse Hyperbolic Functions Overview</a></dt> <dt><a href="math_toolkit/inv_hyper/acosh.html">acosh</a></dt> <dt><a href="math_toolkit/inv_hyper/asinh.html">asinh</a></dt> <dt><a href="math_toolkit/inv_hyper/atanh.html">atanh</a></dt> </dl></dd> <dt><a href="math_toolkit/owens_t.html">Owen's T function</a></dt> </dl> </div> </div> <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> <td align="left"></td> <td align="right"><div class="copyright-footer">Copyright © 2006-2010, 2012-2014 Nikhar Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert Holin, Bruno Lalande, John Maddock, Johan Råde, Gautam Sewani, Benjamin Sobotta, Thijs van den Berg, Daryle Walker and Xiaogang Zhang Distributed under the Boost Software License, Version 1.0. (See accompanying 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>) </div></td> </tr></table> <hr> <div class="spirit-nav"> <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> </div> </body> </html>