| [section:tr1_ref TR1 C Functions Quick Reference] |
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| |
| [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.] |
| |
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| [endsect] |
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| [/ |
| 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). |
| ] |
| |