TR1 Mathematical Special Functions
Numerics
Collaboration diagram for TR1 Mathematical Special Functions:

## Functions

template<typename _Tp>
__gnu_cxx::__promote< _Tp >::__type | std::tr1::assoc_laguerre (unsigned int __n, unsigned int __m, _Tp __x)
float | std::tr1::assoc_laguerref (unsigned int __n, unsigned int __m, float __x)
long double | std::tr1::assoc_laguerrel (unsigned int __n, unsigned int __m, long double __x)
template<typename _Tp>
__gnu_cxx::__promote< _Tp >::__type | std::tr1::assoc_legendre (unsigned int __l, unsigned int __m, _Tp __x)
float | std::tr1::assoc_legendref (unsigned int __l, unsigned int __m, float __x)
long double | std::tr1::assoc_legendrel (unsigned int __l, unsigned int __m, long double __x)
template<typename _Tpx, typename _Tpy>
__gnu_cxx::__promote_2< _Tpx, _Tpy >::__type | std::tr1::beta (_Tpx __x, _Tpy __y)
float | std::tr1::betaf (float __x, float __y)
long double | std::tr1::betal (long double __x, long double __y)
template<typename _Tp>
__gnu_cxx::__promote< _Tp >::__type | std::tr1::comp_ellint_1 (_Tp __k)
float | std::tr1::comp_ellint_1f (float __k)
long double | std::tr1::comp_ellint_1l (long double __k)
template<typename _Tp>
__gnu_cxx::__promote< _Tp >::__type | std::tr1::comp_ellint_2 (_Tp __k)
float | std::tr1::comp_ellint_2f (float __k)
long double | std::tr1::comp_ellint_2l (long double __k)
template<typename _Tp, typename _Tpn>
__gnu_cxx::__promote_2< _Tp, _Tpn >::__type | std::tr1::comp_ellint_3 (_Tp __k, _Tpn __nu)
float | std::tr1::comp_ellint_3f (float __k, float __nu)
long double | std::tr1::comp_ellint_3l (long double __k, long double __nu)
template<typename _Tpnu, typename _Tp>
__gnu_cxx::__promote_2< _Tpnu, _Tp >::__type | std::tr1::cyl_bessel_i (_Tpnu __nu, _Tp __x)
float | std::tr1::cyl_bessel_if (float __nu, float __x)
long double | std::tr1::cyl_bessel_il (long double __nu, long double __x)
template<typename _Tpnu, typename _Tp>
__gnu_cxx::__promote_2< _Tpnu, _Tp >::__type | std::tr1::cyl_bessel_j (_Tpnu __nu, _Tp __x)
float | std::tr1::cyl_bessel_jf (float __nu, float __x)
long double | std::tr1::cyl_bessel_jl (long double __nu, long double __x)
template<typename _Tpnu, typename _Tp>
__gnu_cxx::__promote_2< _Tpnu, _Tp >::__type | std::tr1::cyl_bessel_k (_Tpnu __nu, _Tp __x)
float | std::tr1::cyl_bessel_kf (float __nu, float __x)
long double | std::tr1::cyl_bessel_kl (long double __nu, long double __x)
template<typename _Tpnu, typename _Tp>
__gnu_cxx::__promote_2< _Tpnu, _Tp >::__type | std::tr1::cyl_neumann (_Tpnu __nu, _Tp __x)
float | std::tr1::cyl_neumannf (float __nu, float __x)
long double | std::tr1::cyl_neumannl (long double __nu, long double __x)
template<typename _Tp, typename _Tpp>
__gnu_cxx::__promote_2< _Tp, _Tpp >::__type | std::tr1::ellint_1 (_Tp __k, _Tpp __phi)
float | std::tr1::ellint_1f (float __k, float __phi)
long double | std::tr1::ellint_1l (long double __k, long double __phi)
template<typename _Tp, typename _Tpp>
__gnu_cxx::__promote_2< _Tp, _Tpp >::__type | std::tr1::ellint_2 (_Tp __k, _Tpp __phi)
float | std::tr1::ellint_2f (float __k, float __phi)
long double | std::tr1::ellint_2l (long double __k, long double __phi)
template<typename _Tp, typename _Tpn, typename _Tpp>
__gnu_cxx::__promote_3< _Tp, _Tpn, _Tpp >::__type | std::tr1::ellint_3 (_Tp __k, _Tpn __nu, _Tpp __phi)
float | std::tr1::ellint_3f (float __k, float __nu, float __phi)
long double | std::tr1::ellint_3l (long double __k, long double __nu, long double __phi)
template<typename _Tp>
__gnu_cxx::__promote< _Tp >::__type | std::tr1::expint (_Tp __x)
float | std::tr1::expintf (float __x)
long double | std::tr1::expintl (long double __x)
template<typename _Tp>
__gnu_cxx::__promote< _Tp >::__type | std::tr1::hermite (unsigned int __n, _Tp __x)
float | std::tr1::hermitef (unsigned int __n, float __x)
long double | std::tr1::hermitel (unsigned int __n, long double __x)
template<typename _Tp>
__gnu_cxx::__promote< _Tp >::__type | std::tr1::laguerre (unsigned int __n, _Tp __x)
float | std::tr1::laguerref (unsigned int __n, float __x)
long double | std::tr1::laguerrel (unsigned int __n, long double __x)
template<typename _Tp>
__gnu_cxx::__promote< _Tp >::__type | std::tr1::legendre (unsigned int __n, _Tp __x)
float | std::tr1::legendref (unsigned int __n, float __x)
long double | std::tr1::legendrel (unsigned int __n, long double __x)
template<typename _Tp>
__gnu_cxx::__promote< _Tp >::__type | std::tr1::riemann_zeta (_Tp __x)
float | std::tr1::riemann_zetaf (float __x)
long double | std::tr1::riemann_zetal (long double __x)
template<typename _Tp>
__gnu_cxx::__promote< _Tp >::__type | std::tr1::sph_bessel (unsigned int __n, _Tp __x)
float | std::tr1::sph_besself (unsigned int __n, float __x)
long double | std::tr1::sph_bessell (unsigned int __n, long double __x)
template<typename _Tp>
__gnu_cxx::__promote< _Tp >::__type | std::tr1::sph_legendre (unsigned int __l, unsigned int __m, _Tp __theta)
float | std::tr1::sph_legendref (unsigned int __l, unsigned int __m, float __theta)
long double | std::tr1::sph_legendrel (unsigned int __l, unsigned int __m, long double __theta)
template<typename _Tp>
__gnu_cxx::__promote< _Tp >::__type | std::tr1::sph_neumann (unsigned int __n, _Tp __x)
float | std::tr1::sph_neumannf (unsigned int __n, float __x)
long double | std::tr1::sph_neumannl (unsigned int __n, long double __x)

## Detailed Description

A collection of advanced mathematical special functions.

## Function Documentation

## assoc_laguerre()

template<typename _Tp>

__gnu_cxx::__promote< _Tp >::__type std::tr1::assoc_laguerre | ( | unsigned int | __n,
|  | unsigned int | __m,
|  | _Tp | __x )

inline

5.2.1.1 Associated Laguerre polynomials.

Definition at line 1283 of file tr1/cmath.

## assoc_laguerref()

float std::tr1::assoc_laguerref | ( | unsigned int | __n,
|  | unsigned int | __m,
|  | float | __x )

inline

Definition at line 1271 of file tr1/cmath.

## assoc_laguerrel()

long double std::tr1::assoc_laguerrel | ( | unsigned int | __n,
|  | unsigned int | __m,
|  | long double | __x )

inline

Definition at line 1275 of file tr1/cmath.

## assoc_legendre()

template<typename _Tp>

__gnu_cxx::__promote< _Tp >::__type std::tr1::assoc_legendre | ( | unsigned int | __l,
|  | unsigned int | __m,
|  | _Tp | __x )

inline

5.2.1.2 Associated Legendre functions.

Definition at line 1300 of file tr1/cmath.

## assoc_legendref()

float std::tr1::assoc_legendref | ( | unsigned int | __l,
|  | unsigned int | __m,
|  | float | __x )

inline

Definition at line 1290 of file tr1/cmath.

## assoc_legendrel()

long double std::tr1::assoc_legendrel | ( | unsigned int | __l,
|  | unsigned int | __m,
|  | long double | __x )

inline

Definition at line 1294 of file tr1/cmath.

## beta()

template<typename _Tpx, typename _Tpy>

__gnu_cxx::__promote_2< _Tpx, _Tpy >::__type std::tr1::beta | ( | _Tpx | __x,
|  | _Tpy | __y )

inline

5.2.1.3 Beta functions.

Definition at line 1317 of file tr1/cmath.

## betaf()

float std::tr1::betaf | ( | float | __x,
|  | float | __y )

inline

Definition at line 1307 of file tr1/cmath.

## betal()

long double std::tr1::betal | ( | long double | __x,
|  | long double | __y )

inline

Definition at line 1311 of file tr1/cmath.

## comp_ellint_1()

template<typename _Tp>

__gnu_cxx::__promote< _Tp >::__type std::tr1::comp_ellint_1 | ( | _Tp | __k | ) |

inline

5.2.1.4 Complete elliptic integrals of the first kind.

Definition at line 1334 of file tr1/cmath.

## comp_ellint_1f()

float std::tr1::comp_ellint_1f | ( | float | __k | ) |

inline

Definition at line 1324 of file tr1/cmath.

## comp_ellint_1l()

long double std::tr1::comp_ellint_1l | ( | long double | __k | ) |

inline

Definition at line 1328 of file tr1/cmath.

## comp_ellint_2()

template<typename _Tp>

__gnu_cxx::__promote< _Tp >::__type std::tr1::comp_ellint_2 | ( | _Tp | __k | ) |

inline

5.2.1.5 Complete elliptic integrals of the second kind.

Definition at line 1351 of file tr1/cmath.

## comp_ellint_2f()

float std::tr1::comp_ellint_2f | ( | float | __k | ) |

inline

Definition at line 1341 of file tr1/cmath.

## comp_ellint_2l()

long double std::tr1::comp_ellint_2l | ( | long double | __k | ) |

inline

Definition at line 1345 of file tr1/cmath.

## comp_ellint_3()

template<typename _Tp, typename _Tpn>

__gnu_cxx::__promote_2< _Tp, _Tpn >::__type std::tr1::comp_ellint_3 | ( | _Tp | __k,
|  | _Tpn | __nu )

inline

5.2.1.6 Complete elliptic integrals of the third kind.

Definition at line 1368 of file tr1/cmath.

## comp_ellint_3f()

float std::tr1::comp_ellint_3f | ( | float | __k,
|  | float | __nu )

inline

Definition at line 1358 of file tr1/cmath.

## comp_ellint_3l()

long double std::tr1::comp_ellint_3l | ( | long double | __k,
|  | long double | __nu )

inline

Definition at line 1362 of file tr1/cmath.

## cyl_bessel_i()

template<typename _Tpnu, typename _Tp>

__gnu_cxx::__promote_2< _Tpnu, _Tp >::__type std::tr1::cyl_bessel_i | ( | _Tpnu | __nu,
|  | _Tp | __x )

inline

5.2.1.8 Regular modified cylindrical Bessel functions.

Definition at line 1385 of file tr1/cmath.

## cyl_bessel_if()

float std::tr1::cyl_bessel_if | ( | float | __nu,
|  | float | __x )

inline

Definition at line 1375 of file tr1/cmath.

## cyl_bessel_il()

long double std::tr1::cyl_bessel_il | ( | long double | __nu,
|  | long double | __x )

inline

Definition at line 1379 of file tr1/cmath.

## cyl_bessel_j()

template<typename _Tpnu, typename _Tp>

__gnu_cxx::__promote_2< _Tpnu, _Tp >::__type std::tr1::cyl_bessel_j | ( | _Tpnu | __nu,
|  | _Tp | __x )

inline

5.2.1.9 Cylindrical Bessel functions (of the first kind).

Definition at line 1402 of file tr1/cmath.

## cyl_bessel_jf()

float std::tr1::cyl_bessel_jf | ( | float | __nu,
|  | float | __x )

inline

Definition at line 1392 of file tr1/cmath.

## cyl_bessel_jl()

long double std::tr1::cyl_bessel_jl | ( | long double | __nu,
|  | long double | __x )

inline

Definition at line 1396 of file tr1/cmath.

## cyl_bessel_k()

template<typename _Tpnu, typename _Tp>

__gnu_cxx::__promote_2< _Tpnu, _Tp >::__type std::tr1::cyl_bessel_k | ( | _Tpnu | __nu,
|  | _Tp | __x )

inline

5.2.1.10 Irregular modified cylindrical Bessel functions.

Definition at line 1419 of file tr1/cmath.

## cyl_bessel_kf()

float std::tr1::cyl_bessel_kf | ( | float | __nu,
|  | float | __x )

inline

Definition at line 1409 of file tr1/cmath.

## cyl_bessel_kl()

long double std::tr1::cyl_bessel_kl | ( | long double | __nu,
|  | long double | __x )

inline

Definition at line 1413 of file tr1/cmath.

## cyl_neumann()

template<typename _Tpnu, typename _Tp>

__gnu_cxx::__promote_2< _Tpnu, _Tp >::__type std::tr1::cyl_neumann | ( | _Tpnu | __nu,
|  | _Tp | __x )

inline

5.2.1.11 Cylindrical Neumann functions.

Definition at line 1436 of file tr1/cmath.

## cyl_neumannf()

float std::tr1::cyl_neumannf | ( | float | __nu,
|  | float | __x )

inline

Definition at line 1426 of file tr1/cmath.

## cyl_neumannl()

long double std::tr1::cyl_neumannl | ( | long double | __nu,
|  | long double | __x )

inline

Definition at line 1430 of file tr1/cmath.

## ellint_1()

template<typename _Tp, typename _Tpp>

__gnu_cxx::__promote_2< _Tp, _Tpp >::__type std::tr1::ellint_1 | ( | _Tp | __k,
|  | _Tpp | __phi )

inline

5.2.1.12 Incomplete elliptic integrals of the first kind.

Definition at line 1453 of file tr1/cmath.

## ellint_1f()

float std::tr1::ellint_1f | ( | float | __k,
|  | float | __phi )

inline

Definition at line 1443 of file tr1/cmath.

## ellint_1l()

long double std::tr1::ellint_1l | ( | long double | __k,
|  | long double | __phi )

inline

Definition at line 1447 of file tr1/cmath.

## ellint_2()

template<typename _Tp, typename _Tpp>

__gnu_cxx::__promote_2< _Tp, _Tpp >::__type std::tr1::ellint_2 | ( | _Tp | __k,
|  | _Tpp | __phi )

inline

5.2.1.13 Incomplete elliptic integrals of the second kind.

Definition at line 1470 of file tr1/cmath.

## ellint_2f()

float std::tr1::ellint_2f | ( | float | __k,
|  | float | __phi )

inline

Definition at line 1460 of file tr1/cmath.

## ellint_2l()

long double std::tr1::ellint_2l | ( | long double | __k,
|  | long double | __phi )

inline

Definition at line 1464 of file tr1/cmath.

## ellint_3()

template<typename _Tp, typename _Tpn, typename _Tpp>

__gnu_cxx::__promote_3< _Tp, _Tpn, _Tpp >::__type std::tr1::ellint_3 | ( | _Tp | __k,
|  | _Tpn | __nu,
|  | _Tpp | __phi )

inline

5.2.1.14 Incomplete elliptic integrals of the third kind.

Definition at line 1487 of file tr1/cmath.

## ellint_3f()

float std::tr1::ellint_3f | ( | float | __k,
|  | float | __nu,
|  | float | __phi )

inline

Definition at line 1477 of file tr1/cmath.

## ellint_3l()

long double std::tr1::ellint_3l | ( | long double | __k,
|  | long double | __nu,
|  | long double | __phi )

inline

Definition at line 1481 of file tr1/cmath.

## expint()

template<typename _Tp>

__gnu_cxx::__promote< _Tp >::__type std::tr1::expint | ( | _Tp | __x | ) |

inline

5.2.1.15 Exponential integrals.

Definition at line 1504 of file tr1/cmath.

## expintf()

float std::tr1::expintf | ( | float | __x | ) |

inline

Definition at line 1494 of file tr1/cmath.

## expintl()

long double std::tr1::expintl | ( | long double | __x | ) |

inline

Definition at line 1498 of file tr1/cmath.

## hermite()

template<typename _Tp>

__gnu_cxx::__promote< _Tp >::__type std::tr1::hermite | ( | unsigned int | __n,
|  | _Tp | __x )

inline

5.2.1.16 Hermite polynomials.

Definition at line 1521 of file tr1/cmath.

## hermitef()

float std::tr1::hermitef | ( | unsigned int | __n,
|  | float | __x )

inline

Definition at line 1511 of file tr1/cmath.

## hermitel()

long double std::tr1::hermitel | ( | unsigned int | __n,
|  | long double | __x )

inline

Definition at line 1515 of file tr1/cmath.

## laguerre()

template<typename _Tp>

__gnu_cxx::__promote< _Tp >::__type std::tr1::laguerre | ( | unsigned int | __n,
|  | _Tp | __x )

inline

5.2.1.18 Laguerre polynomials.

Definition at line 1538 of file tr1/cmath.

## laguerref()

float std::tr1::laguerref | ( | unsigned int | __n,
|  | float | __x )

inline

Definition at line 1528 of file tr1/cmath.

## laguerrel()

long double std::tr1::laguerrel | ( | unsigned int | __n,
|  | long double | __x )

inline

Definition at line 1532 of file tr1/cmath.

## legendre()

template<typename _Tp>

__gnu_cxx::__promote< _Tp >::__type std::tr1::legendre | ( | unsigned int | __n,
|  | _Tp | __x )

inline

5.2.1.19 Legendre polynomials.

Definition at line 1555 of file tr1/cmath.

## legendref()

float std::tr1::legendref | ( | unsigned int | __n,
|  | float | __x )

inline

Definition at line 1545 of file tr1/cmath.

## legendrel()

long double std::tr1::legendrel | ( | unsigned int | __n,
|  | long double | __x )

inline

Definition at line 1549 of file tr1/cmath.

## riemann_zeta()

template<typename _Tp>

__gnu_cxx::__promote< _Tp >::__type std::tr1::riemann_zeta | ( | _Tp | __x | ) |

inline

5.2.1.20 Riemann zeta function.

Definition at line 1572 of file tr1/cmath.

## riemann_zetaf()

float std::tr1::riemann_zetaf | ( | float | __x | ) |

inline

Definition at line 1562 of file tr1/cmath.

## riemann_zetal()

long double std::tr1::riemann_zetal | ( | long double | __x | ) |

inline

Definition at line 1566 of file tr1/cmath.

## sph_bessel()

template<typename _Tp>

__gnu_cxx::__promote< _Tp >::__type std::tr1::sph_bessel | ( | unsigned int | __n,
|  | _Tp | __x )

inline

5.2.1.21 Spherical Bessel functions.

Definition at line 1589 of file tr1/cmath.

## sph_besself()

float std::tr1::sph_besself | ( | unsigned int | __n,
|  | float | __x )

inline

Definition at line 1579 of file tr1/cmath.

## sph_bessell()

long double std::tr1::sph_bessell | ( | unsigned int | __n,
|  | long double | __x )

inline

Definition at line 1583 of file tr1/cmath.

## sph_legendre()

template<typename _Tp>

__gnu_cxx::__promote< _Tp >::__type std::tr1::sph_legendre | ( | unsigned int | __l,
|  | unsigned int | __m,
|  | _Tp | __theta )

inline

5.2.1.22 Spherical associated Legendre functions.

Definition at line 1606 of file tr1/cmath.

## sph_legendref()

float std::tr1::sph_legendref | ( | unsigned int | __l,
|  | unsigned int | __m,
|  | float | __theta )

inline

Definition at line 1596 of file tr1/cmath.

## sph_legendrel()

long double std::tr1::sph_legendrel | ( | unsigned int | __l,
|  | unsigned int | __m,
|  | long double | __theta )

inline

Definition at line 1600 of file tr1/cmath.

## sph_neumann()

template<typename _Tp>

__gnu_cxx::__promote< _Tp >::__type std::tr1::sph_neumann | ( | unsigned int | __n,
|  | _Tp | __x )

inline

5.2.1.23 Spherical Neumann functions.

Definition at line 1623 of file tr1/cmath.

## sph_neumannf()

float std::tr1::sph_neumannf | ( | unsigned int | __n,
|  | float | __x )

inline

Definition at line 1613 of file tr1/cmath.

## sph_neumannl()

long double std::tr1::sph_neumannl | ( | unsigned int | __n,
|  | long double | __x )

inline

Definition at line 1617 of file tr1/cmath.