Mathematical Special Functions
[Numerics]

Collaboration diagram for 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 _Tpa , typename _Tpc , typename _Tp > __gnu_cxx::__promote_3< _Tpa,
  _Tpc, _Tp >::__type std::tr1::conf_hyperg (_Tpa __a, _Tpc __c, _Tp __x)
• float std::tr1::conf_hypergf (float __a, float __c, float __x)
• long double std::tr1::conf_hypergl (long double __a, long double __c, long double __x)
• 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 _Tpa , typename _Tpb , typename _Tpc , typename _Tp > __gnu_cxx::__promote_4< _Tpa,
  _Tpb, _Tpc, _Tp >::__type std::tr1::hyperg (_Tpa __a, _Tpb __b, _Tpc __c, _Tp __x)
• float std::tr1::hypergf (float __a, float __b, float __c, float __x)
• long double std::tr1::hypergl (long double __a, long double __b, long double __c, 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

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 123 of file tr1/cmath.

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 140 of file tr1/cmath.

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 157 of file tr1/cmath.

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 174 of file tr1/cmath.

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 191 of file tr1/cmath.

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 208 of file tr1/cmath.

template<typename _Tpa , typename _Tpc , typename _Tp >

__gnu_cxx::__promote_3<_Tpa, _Tpc, _Tp>::__type std::tr1::conf_hyperg	(	_Tpa	__a,
		_Tpc	__c,
		_Tp	__x
	)			[inline]

5.2.1.7 Confluent hypergeometric functions.

Definition at line 225 of file tr1/cmath.

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 242 of file tr1/cmath.

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 259 of file tr1/cmath.

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 276 of file tr1/cmath.

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 293 of file tr1/cmath.

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 310 of file tr1/cmath.

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 327 of file tr1/cmath.

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 344 of file tr1/cmath.

template<typename _Tp >

__gnu_cxx::__promote<_Tp>::__type std::tr1::expint

(

_Tp

__x

)

[inline]

5.2.1.15 Exponential integrals.

Definition at line 361 of file tr1/cmath.

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 378 of file tr1/cmath.

template<typename _Tpa , typename _Tpb , typename _Tpc , typename _Tp >

__gnu_cxx::__promote_4<_Tpa, _Tpb, _Tpc, _Tp>::__type std::tr1::hyperg	(	_Tpa	__a,
		_Tpb	__b,
		_Tpc	__c,
		_Tp	__x
	)			[inline]

5.2.1.17 Hypergeometric functions.

Definition at line 395 of file tr1/cmath.

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 412 of file tr1/cmath.

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 429 of file tr1/cmath.

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 446 of file tr1/cmath.

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 463 of file tr1/cmath.

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 480 of file tr1/cmath.

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 497 of file tr1/cmath.