[section:tr1_ref TR1 C Functions Quick Reference] [h4 Supported TR1 Functions] namespace boost{ namespace math{ namespace tr1{ extern "C"{ // [5.2.1.1] associated Laguerre polynomials: double assoc_laguerre(unsigned n, unsigned m, double x); float assoc_laguerref(unsigned n, unsigned m, float x); long double assoc_laguerrel(unsigned n, unsigned m, long double x); // [5.2.1.2] associated Legendre functions: double assoc_legendre(unsigned l, unsigned m, double x); float assoc_legendref(unsigned l, unsigned m, float x); long double assoc_legendrel(unsigned l, unsigned m, long double x); // [5.2.1.3] beta function: double beta(double x, double y); float betaf(float x, float y); long double betal(long double x, long double y); // [5.2.1.4] (complete) elliptic integral of the first kind: double comp_ellint_1(double k); float comp_ellint_1f(float k); long double comp_ellint_1l(long double k); // [5.2.1.5] (complete) elliptic integral of the second kind: double comp_ellint_2(double k); float comp_ellint_2f(float k); long double comp_ellint_2l(long double k); // [5.2.1.6] (complete) elliptic integral of the third kind: double comp_ellint_3(double k, double nu); float comp_ellint_3f(float k, float nu); long double comp_ellint_3l(long double k, long double nu); // [5.2.1.8] regular modified cylindrical Bessel functions: double cyl_bessel_i(double nu, double x); float cyl_bessel_if(float nu, float x); long double cyl_bessel_il(long double nu, long double x); // [5.2.1.9] cylindrical Bessel functions (of the first kind): double cyl_bessel_j(double nu, double x); float cyl_bessel_jf(float nu, float x); long double cyl_bessel_jl(long double nu, long double x); // [5.2.1.10] irregular modified cylindrical Bessel functions: double cyl_bessel_k(double nu, double x); float cyl_bessel_kf(float nu, float x); long double cyl_bessel_kl(long double nu, long double x); // [5.2.1.11] cylindrical Neumann functions; // cylindrical Bessel functions (of the second kind): double cyl_neumann(double nu, double x); float cyl_neumannf(float nu, float x); long double cyl_neumannl(long double nu, long double x); // [5.2.1.12] (incomplete) elliptic integral of the first kind: double ellint_1(double k, double phi); float ellint_1f(float k, float phi); long double ellint_1l(long double k, long double phi); // [5.2.1.13] (incomplete) elliptic integral of the second kind: double ellint_2(double k, double phi); float ellint_2f(float k, float phi); long double ellint_2l(long double k, long double phi); // [5.2.1.14] (incomplete) elliptic integral of the third kind: double ellint_3(double k, double nu, double phi); float ellint_3f(float k, float nu, float phi); long double ellint_3l(long double k, long double nu, long double phi); // [5.2.1.15] exponential integral: double expint(double x); float expintf(float x); long double expintl(long double x); // [5.2.1.16] Hermite polynomials: double hermite(unsigned n, double x); float hermitef(unsigned n, float x); long double hermitel(unsigned n, long double x); // [5.2.1.18] Laguerre polynomials: double laguerre(unsigned n, double x); float laguerref(unsigned n, float x); long double laguerrel(unsigned n, long double x); // [5.2.1.19] Legendre polynomials: double legendre(unsigned l, double x); float legendref(unsigned l, float x); long double legendrel(unsigned l, long double x); // [5.2.1.20] Riemann zeta function: double riemann_zeta(double); float riemann_zetaf(float); long double riemann_zetal(long double); // [5.2.1.21] spherical Bessel functions (of the first kind): double sph_bessel(unsigned n, double x); float sph_besself(unsigned n, float x); long double sph_bessell(unsigned n, long double x); // [5.2.1.22] spherical associated Legendre functions: double sph_legendre(unsigned l, unsigned m, double theta); float sph_legendref(unsigned l, unsigned m, float theta); long double sph_legendrel(unsigned l, unsigned m, long double theta); // [5.2.1.23] spherical Neumann functions; // spherical Bessel functions (of the second kind): double sph_neumann(unsigned n, double x); float sph_neumannf(unsigned n, float x); long double sph_neumannl(unsigned n, long double x); }}}} // namespaces In addition sufficient additional overloads of the `double` versions of the above functions are provided, so that calling the function with any mixture of `float`, `double`, `long double`, or /integer/ arguments is supported, with the return type determined by the __arg_pomotion_rules. For example: expintf(2.0f); // float version, returns float. expint(2.0f); // also calls the float version and returns float. expint(2.0); // double version, returns double. expintl(2.0L); // long double version, returns a long double. expint(2.0L); // also calls the long double version. expint(2); // integer argument is treated as a double, returns double. [h4 Quick Reference] // [5.2.1.1] associated Laguerre polynomials: double assoc_laguerre(unsigned n, unsigned m, double x); float assoc_laguerref(unsigned n, unsigned m, float x); long double assoc_laguerrel(unsigned n, unsigned m, long double x); The assoc_laguerre functions return: [equation laguerre_1] See also __laguerre for the full template (header only) version of this function. // [5.2.1.2] associated Legendre functions: double assoc_legendre(unsigned l, unsigned m, double x); float assoc_legendref(unsigned l, unsigned m, float x); long double assoc_legendrel(unsigned l, unsigned m, long double x); The assoc_legendre functions return: [equation legendre_1b] See also __legendre for the full template (header only) version of this function. // [5.2.1.3] beta function: double beta(double x, double y); float betaf(float x, float y); long double betal(long double x, long double y); Returns the beta function of /x/ and /y/: [equation beta1] See also __beta for the full template (header only) version of this function. // [5.2.1.4] (complete) elliptic integral of the first kind: double comp_ellint_1(double k); float comp_ellint_1f(float k); long double comp_ellint_1l(long double k); Returns the complete elliptic integral of the first kind of /k/: [equation ellint6] See also __ellint_1 for the full template (header only) version of this function. // [5.2.1.5] (complete) elliptic integral of the second kind: double comp_ellint_2(double k); float comp_ellint_2f(float k); long double comp_ellint_2l(long double k); Returns the complete elliptic integral of the second kind of /k/: [equation ellint7] See also __ellint_2 for the full template (header only) version of this function. // [5.2.1.6] (complete) elliptic integral of the third kind: double comp_ellint_3(double k, double nu); float comp_ellint_3f(float k, float nu); long double comp_ellint_3l(long double k, long double nu); Returns the complete elliptic integral of the third kind of /k/ and /nu/: [equation ellint8] See also __ellint_3 for the full template (header only) version of this function. // [5.2.1.8] regular modified cylindrical Bessel functions: double cyl_bessel_i(double nu, double x); float cyl_bessel_if(float nu, float x); long double cyl_bessel_il(long double nu, long double x); Returns the modified bessel function of the first kind of /nu/ and /x/: [equation mbessel2] See also __cyl_bessel_i for the full template (header only) version of this function. // [5.2.1.9] cylindrical Bessel functions (of the first kind): double cyl_bessel_j(double nu, double x); float cyl_bessel_jf(float nu, float x); long double cyl_bessel_jl(long double nu, long double x); Returns the bessel function of the first kind of /nu/ and /x/: [equation bessel2] See also __cyl_bessel_j for the full template (header only) version of this function. // [5.2.1.10] irregular modified cylindrical Bessel functions: double cyl_bessel_k(double nu, double x); float cyl_bessel_kf(float nu, float x); long double cyl_bessel_kl(long double nu, long double x); Returns the modified bessel function of the second kind of /nu/ and /x/: [equation mbessel3] See also __cyl_bessel_k for the full template (header only) version of this function. // [5.2.1.11] cylindrical Neumann functions; // cylindrical Bessel functions (of the second kind): double cyl_neumann(double nu, double x); float cyl_neumannf(float nu, float x); long double cyl_neumannl(long double nu, long double x); Returns the bessel function of the second kind (Neumann function) of /nu/ and /x/: [equation bessel3] See also __cyl_neumann for the full template (header only) version of this function. // [5.2.1.12] (incomplete) elliptic integral of the first kind: double ellint_1(double k, double phi); float ellint_1f(float k, float phi); long double ellint_1l(long double k, long double phi); Returns the incomplete elliptic integral of the first kind of /k/ and /phi/: [equation ellint2] See also __ellint_1 for the full template (header only) version of this function. // [5.2.1.13] (incomplete) elliptic integral of the second kind: double ellint_2(double k, double phi); float ellint_2f(float k, float phi); long double ellint_2l(long double k, long double phi); Returns the incomplete elliptic integral of the second kind of /k/ and /phi/: [equation ellint3] See also __ellint_2 for the full template (header only) version of this function. // [5.2.1.14] (incomplete) elliptic integral of the third kind: double ellint_3(double k, double nu, double phi); float ellint_3f(float k, float nu, float phi); long double ellint_3l(long double k, long double nu, long double phi); Returns the incomplete elliptic integral of the third kind of /k/, /nu/ and /phi/: [equation ellint4] See also __ellint_3 for the full template (header only) version of this function. // [5.2.1.15] exponential integral: double expint(double x); float expintf(float x); long double expintl(long double x); Returns the exponential integral Ei of /x/: [equation expint_i_1] See also __expint for the full template (header only) version of this function. // [5.2.1.16] Hermite polynomials: double hermite(unsigned n, double x); float hermitef(unsigned n, float x); long double hermitel(unsigned n, long double x); Returns the n'th Hermite polynomial of /x/: [equation hermite_0] See also __hermite for the full template (header only) version of this function. // [5.2.1.18] Laguerre polynomials: double laguerre(unsigned n, double x); float laguerref(unsigned n, float x); long double laguerrel(unsigned n, long double x); Returns the n'th Laguerre polynomial of /x/: [equation laguerre_0] See also __laguerre for the full template (header only) version of this function. // [5.2.1.19] Legendre polynomials: double legendre(unsigned l, double x); float legendref(unsigned l, float x); long double legendrel(unsigned l, long double x); Returns the l'th Legendre polynomial of /x/: [equation legendre_0] See also __legendre for the full template (header only) version of this function. // [5.2.1.20] Riemann zeta function: double riemann_zeta(double); float riemann_zetaf(float); long double riemann_zetal(long double); Returns the Riemann Zeta function of /x/: [equation zeta1] See also __zeta for the full template (header only) version of this function. // [5.2.1.21] spherical Bessel functions (of the first kind): double sph_bessel(unsigned n, double x); float sph_besself(unsigned n, float x); long double sph_bessell(unsigned n, long double x); Returns the spherical Bessel function of the first kind of /x/ j[sub n](x): [equation sbessel2] See also __sph_bessel for the full template (header only) version of this function. // [5.2.1.22] spherical associated Legendre functions: double sph_legendre(unsigned l, unsigned m, double theta); float sph_legendref(unsigned l, unsigned m, float theta); long double sph_legendrel(unsigned l, unsigned m, long double theta); Returns the spherical associated Legendre function of /l/, /m/ and /theta/: [equation spherical_3] See also __spherical_harmonic for the full template (header only) version of this function. // [5.2.1.23] spherical Neumann functions; // spherical Bessel functions (of the second kind): double sph_neumann(unsigned n, double x); float sph_neumannf(unsigned n, float x); long double sph_neumannl(unsigned n, long double x); Returns the spherical Neumann function of /x/ y[sub n](x): [equation sbessel2] See also __sph_bessel for the full template (header only) version of this function. [h4 Currently Unsupported TR1 Functions] // [5.2.1.7] confluent hypergeometric functions: double conf_hyperg(double a, double c, double x); float conf_hypergf(float a, float c, float x); long double conf_hypergl(long double a, long double c, long double x); // [5.2.1.17] hypergeometric functions: double hyperg(double a, double b, double c, double x); float hypergf(float a, float b, float c, float x); long double hypergl(long double a, long double b, long double c, long double x); [note These two functions are not implemented as they are not believed to be numerically stable.] [endsect] [/ Copyright 2008, 2009 John Maddock and Paul A. Bristow. Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt). ]