libstdc++
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template<typename _Tp > | |
__gnu_cxx::__promote< _Tp >::__type | std::assoc_laguerre (unsigned int __n, unsigned int __m, _Tp __x) |
float | std::assoc_laguerref (unsigned int __n, unsigned int __m, float __x) |
long double | std::assoc_laguerrel (unsigned int __n, unsigned int __m, long double __x) |
template<typename _Tp > | |
__gnu_cxx::__promote< _Tp >::__type | std::assoc_legendre (unsigned int __l, unsigned int __m, _Tp __x) |
float | std::assoc_legendref (unsigned int __l, unsigned int __m, float __x) |
long double | std::assoc_legendrel (unsigned int __l, unsigned int __m, long double __x) |
template<typename _Tpa , typename _Tpb > | |
__gnu_cxx::__promote_2< _Tpa, _Tpb >::__type | std::beta (_Tpa __a, _Tpb __b) |
float | std::betaf (float __a, float __b) |
long double | std::betal (long double __a, long double __b) |
template<typename _Tp > | |
__gnu_cxx::__promote< _Tp >::__type | std::comp_ellint_1 (_Tp __k) |
float | std::comp_ellint_1f (float __k) |
long double | std::comp_ellint_1l (long double __k) |
template<typename _Tp > | |
__gnu_cxx::__promote< _Tp >::__type | std::comp_ellint_2 (_Tp __k) |
float | std::comp_ellint_2f (float __k) |
long double | std::comp_ellint_2l (long double __k) |
template<typename _Tp , typename _Tpn > | |
__gnu_cxx::__promote_2< _Tp, _Tpn >::__type | std::comp_ellint_3 (_Tp __k, _Tpn __nu) |
float | std::comp_ellint_3f (float __k, float __nu) |
long double | std::comp_ellint_3l (long double __k, long double __nu) |
template<typename _Tpnu , typename _Tp > | |
__gnu_cxx::__promote_2< _Tpnu, _Tp >::__type | std::cyl_bessel_i (_Tpnu __nu, _Tp __x) |
float | std::cyl_bessel_if (float __nu, float __x) |
long double | std::cyl_bessel_il (long double __nu, long double __x) |
template<typename _Tpnu , typename _Tp > | |
__gnu_cxx::__promote_2< _Tpnu, _Tp >::__type | std::cyl_bessel_j (_Tpnu __nu, _Tp __x) |
float | std::cyl_bessel_jf (float __nu, float __x) |
long double | std::cyl_bessel_jl (long double __nu, long double __x) |
template<typename _Tpnu , typename _Tp > | |
__gnu_cxx::__promote_2< _Tpnu, _Tp >::__type | std::cyl_bessel_k (_Tpnu __nu, _Tp __x) |
float | std::cyl_bessel_kf (float __nu, float __x) |
long double | std::cyl_bessel_kl (long double __nu, long double __x) |
template<typename _Tpnu , typename _Tp > | |
__gnu_cxx::__promote_2< _Tpnu, _Tp >::__type | std::cyl_neumann (_Tpnu __nu, _Tp __x) |
float | std::cyl_neumannf (float __nu, float __x) |
long double | std::cyl_neumannl (long double __nu, long double __x) |
template<typename _Tp , typename _Tpp > | |
__gnu_cxx::__promote_2< _Tp, _Tpp >::__type | std::ellint_1 (_Tp __k, _Tpp __phi) |
float | std::ellint_1f (float __k, float __phi) |
long double | std::ellint_1l (long double __k, long double __phi) |
template<typename _Tp , typename _Tpp > | |
__gnu_cxx::__promote_2< _Tp, _Tpp >::__type | std::ellint_2 (_Tp __k, _Tpp __phi) |
float | std::ellint_2f (float __k, float __phi) |
long double | std::ellint_2l (long double __k, long double __phi) |
template<typename _Tp , typename _Tpn , typename _Tpp > | |
__gnu_cxx::__promote_3< _Tp, _Tpn, _Tpp >::__type | std::ellint_3 (_Tp __k, _Tpn __nu, _Tpp __phi) |
float | std::ellint_3f (float __k, float __nu, float __phi) |
long double | std::ellint_3l (long double __k, long double __nu, long double __phi) |
template<typename _Tp > | |
__gnu_cxx::__promote< _Tp >::__type | std::expint (_Tp __x) |
float | std::expintf (float __x) |
long double | std::expintl (long double __x) |
template<typename _Tp > | |
__gnu_cxx::__promote< _Tp >::__type | std::hermite (unsigned int __n, _Tp __x) |
float | std::hermitef (unsigned int __n, float __x) |
long double | std::hermitel (unsigned int __n, long double __x) |
template<typename _Tp > | |
__gnu_cxx::__promote< _Tp >::__type | std::laguerre (unsigned int __n, _Tp __x) |
float | std::laguerref (unsigned int __n, float __x) |
long double | std::laguerrel (unsigned int __n, long double __x) |
template<typename _Tp > | |
__gnu_cxx::__promote< _Tp >::__type | std::legendre (unsigned int __l, _Tp __x) |
float | std::legendref (unsigned int __l, float __x) |
long double | std::legendrel (unsigned int __l, long double __x) |
template<typename _Tp > | |
__gnu_cxx::__promote< _Tp >::__type | std::riemann_zeta (_Tp __s) |
float | std::riemann_zetaf (float __s) |
long double | std::riemann_zetal (long double __s) |
template<typename _Tp > | |
__gnu_cxx::__promote< _Tp >::__type | std::sph_bessel (unsigned int __n, _Tp __x) |
float | std::sph_besself (unsigned int __n, float __x) |
long double | std::sph_bessell (unsigned int __n, long double __x) |
template<typename _Tp > | |
__gnu_cxx::__promote< _Tp >::__type | std::sph_legendre (unsigned int __l, unsigned int __m, _Tp __theta) |
float | std::sph_legendref (unsigned int __l, unsigned int __m, float __theta) |
long double | std::sph_legendrel (unsigned int __l, unsigned int __m, long double __theta) |
template<typename _Tp > | |
__gnu_cxx::__promote< _Tp >::__type | std::sph_neumann (unsigned int __n, _Tp __x) |
float | std::sph_neumannf (unsigned int __n, float __x) |
long double | std::sph_neumannl (unsigned int __n, long double __x) |
A collection of advanced mathematical special functions, defined by ISO/IEC IS 29124.
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Return the associated Laguerre polynomial of nonnegative order n
, nonnegative degree m
and real argument x:
.
The associated Laguerre function of real degree ,
, is defined by
where is the Pochhammer symbol and
is the confluent hypergeometric function.
The associated Laguerre polynomial is defined for integral degree by:
where the Laguerre polynomial is defined by:
and .
n
_Tp | The floating-point type of the argument __x . |
__n | The order of the Laguerre function, __n >= 0 . |
__m | The degree of the Laguerre function, __m >= 0 . |
__x | The argument of the Laguerre function, __x >= 0 . |
std::domain_error | if __x < 0 . |
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Return the associated Legendre function of degree l
and order m
.
The associated Legendre function is derived from the Legendre function by the Rodrigues formula:
l
_Tp | The floating-point type of the argument __x . |
__l | The degree __l >= 0 . |
__m | The order __m <= l . |
__x | The argument, abs(__x) <= 1 . |
std::domain_error | if abs(__x) > 1 . |
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Return the beta function, , for real parameters
a
, b
.
The beta function is defined by
where and
_Tpa | The floating-point type of the parameter __a . |
_Tpb | The floating-point type of the parameter __b . |
__a | The first argument of the beta function, __a > 0 . |
__b | The second argument of the beta function, __b > 0 . |
std::domain_error | if __a < 0 or __b < 0 . |
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Return the complete elliptic integral of the first kind for real modulus
k
.
The complete elliptic integral of the first kind is defined as
where is the incomplete elliptic integral of the first kind and the modulus
.
_Tp | The floating-point type of the modulus __k . |
__k | The modulus, abs(__k) <= 1 |
std::domain_error | if abs(__k) > 1 . |
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Return the complete elliptic integral of the second kind for real modulus
k
.
The complete elliptic integral of the second kind is defined as
where is the incomplete elliptic integral of the second kind and the modulus
.
_Tp | The floating-point type of the modulus __k . |
__k | The modulus, abs(__k) <= 1 |
std::domain_error | if abs(__k) > 1. |
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Return the complete elliptic integral of the third kind for real modulus
k
.
The complete elliptic integral of the third kind is defined as
where is the incomplete elliptic integral of the second kind and the modulus
.
_Tp | The floating-point type of the modulus __k . |
_Tpn | The floating-point type of the argument __nu . |
__k | The modulus, abs(__k) <= 1 |
__nu | The argument |
std::domain_error | if abs(__k) > 1. |
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Return the regular modified Bessel function for real order
and argument
.
The regular modified cylindrical Bessel function is:
_Tpnu | The floating-point type of the order __nu . |
_Tp | The floating-point type of the argument __x . |
__nu | The order |
__x | The argument, __x >= 0 |
std::domain_error | if __x < 0 . |
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Return the Bessel function of real order
and argument
.
The cylindrical Bessel function is:
_Tpnu | The floating-point type of the order __nu . |
_Tp | The floating-point type of the argument __x . |
__nu | The order |
__x | The argument, __x >= 0 |
std::domain_error | if __x < 0 . |
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Return the irregular modified Bessel function of real order
and argument
.
The irregular modified Bessel function is defined by:
where for integral a limit is taken:
. For negative argument we have simply:
_Tpnu | The floating-point type of the order __nu . |
_Tp | The floating-point type of the argument __x . |
__nu | The order |
__x | The argument, __x >= 0 |
std::domain_error | if __x < 0 . |
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Return the Neumann function of real order
and argument
.
The Neumann function is defined by:
where and for integral order
a limit is taken:
.
_Tpnu | The floating-point type of the order __nu . |
_Tp | The floating-point type of the argument __x . |
__nu | The order |
__x | The argument, __x >= 0 |
std::domain_error | if __x < 0 . |
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Return the incomplete elliptic integral of the first kind for
real
modulus and angle
.
The incomplete elliptic integral of the first kind is defined as
For this becomes the complete elliptic integral of the first kind,
.
_Tp | The floating-point type of the modulus __k . |
_Tpp | The floating-point type of the angle __phi . |
__k | The modulus, abs(__k) <= 1 |
__phi | The integral limit argument in radians |
std::domain_error | if abs(__k) > 1 . |
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Return the incomplete elliptic integral of the second kind .
The incomplete elliptic integral of the second kind is defined as
For this becomes the complete elliptic integral of the second kind,
.
_Tp | The floating-point type of the modulus __k . |
_Tpp | The floating-point type of the angle __phi . |
__k | The modulus, abs(__k) <= 1 |
__phi | The integral limit argument in radians |
std::domain_error | if abs(__k) > 1 . |
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Return the incomplete elliptic integral of the third kind .
The incomplete elliptic integral of the third kind is defined by:
For this becomes the complete elliptic integral of the third kind,
.
_Tp | The floating-point type of the modulus __k . |
_Tpn | The floating-point type of the argument __nu . |
_Tpp | The floating-point type of the angle __phi . |
__k | The modulus, abs(__k) <= 1 |
__nu | The second argument |
__phi | The integral limit argument in radians |
std::domain_error | if abs(__k) > 1 . |
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Return the Hermite polynomial of order n and
real
argument x
.
The Hermite polynomial is defined by:
The Hermite polynomial obeys a reflection formula:
_Tp | The floating-point type of the argument __x . |
__n | The order |
__x | The argument |
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Returns the Laguerre polynomial of nonnegative degree
n
and real argument .
The Laguerre polynomial is defined by:
_Tp | The floating-point type of the argument __x . |
__n | The nonnegative order |
__x | The argument __x >= 0 |
std::domain_error | if __x < 0 . |
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Return the Legendre polynomial of nonnegative degree
and real argument
.
The Legendre function of order and argument
,
, is defined by:
_Tp | The floating-point type of the argument __x . |
__l | The degree ![]() |
__x | The argument abs(__x) <= 1 |
std::domain_error | if abs(__x) > 1 |
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Return the spherical Bessel function of nonnegative order n and real argument
.
The spherical Bessel function is defined by:
_Tp | The floating-point type of the argument __x . |
__n | The integral order n >= 0 |
__x | The real argument x >= 0 |
std::domain_error | if __x < 0 . |
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Return the spherical Legendre function of nonnegative integral degree l
and order m
and real angle in radians.
The spherical Legendre function is defined by
_Tp | The floating-point type of the angle __theta . |
__l | The order __l >= 0 |
__m | The degree __m >= 0 and __m <= __l |
__theta | The radian polar angle argument |
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Return the spherical Neumann function of integral order and real argument
.
The spherical Neumann function is defined by
_Tp | The floating-point type of the argument __x . |
__n | The integral order n >= 0 |
__x | The real argument __x >= 0 |
std::domain_error | if __x < 0 . |
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