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