libstdc++
|
Functions | |
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.
__gnu_cxx::__promote<_Tp>::__type std::assoc_laguerre | ( | unsigned int | __n, |
unsigned int | __m, | ||
_Tp | __x | ||
) | [inline] |
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 . |
float std::assoc_laguerref | ( | unsigned int | __n, |
unsigned int | __m, | ||
float | __x | ||
) | [inline] |
Return the associated Laguerre polynomial of order n
, degree m:
for
float
argument.
long double std::assoc_laguerrel | ( | unsigned int | __n, |
unsigned int | __m, | ||
long double | __x | ||
) | [inline] |
Return the associated Laguerre polynomial of order n
, degree m:
.
__gnu_cxx::__promote<_Tp>::__type std::assoc_legendre | ( | unsigned int | __l, |
unsigned int | __m, | ||
_Tp | __x | ||
) | [inline] |
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 . |
float std::assoc_legendref | ( | unsigned int | __l, |
unsigned int | __m, | ||
float | __x | ||
) | [inline] |
Return the associated Legendre function of degree l
and order m
for float
argument.
long double std::assoc_legendrel | ( | unsigned int | __l, |
unsigned int | __m, | ||
long double | __x | ||
) | [inline] |
Return the associated Legendre function of degree l
and order m
.
__gnu_cxx::__promote_2<_Tpa, _Tpb>::__type std::beta | ( | _Tpa | __a, |
_Tpb | __b | ||
) | [inline] |
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 . |
float std::betaf | ( | float | __a, |
float | __b | ||
) | [inline] |
long double std::betal | ( | long double | __a, |
long double | __b | ||
) | [inline] |
__gnu_cxx::__promote<_Tp>::__type std::comp_ellint_1 | ( | _Tp | __k | ) | [inline] |
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 . |
float std::comp_ellint_1f | ( | float | __k | ) | [inline] |
Return the complete elliptic integral of the first kind for
float
modulus k
.
long double std::comp_ellint_1l | ( | long double | __k | ) | [inline] |
Return the complete elliptic integral of the first kind for long double modulus
k
.
__gnu_cxx::__promote<_Tp>::__type std::comp_ellint_2 | ( | _Tp | __k | ) | [inline] |
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. |
float std::comp_ellint_2f | ( | float | __k | ) | [inline] |
Return the complete elliptic integral of the second kind for
float
modulus k
.
long double std::comp_ellint_2l | ( | long double | __k | ) | [inline] |
Return the complete elliptic integral of the second kind for long double modulus
k
.
__gnu_cxx::__promote_2<_Tp, _Tpn>::__type std::comp_ellint_3 | ( | _Tp | __k, |
_Tpn | __nu | ||
) | [inline] |
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. |
float std::comp_ellint_3f | ( | float | __k, |
float | __nu | ||
) | [inline] |
Return the complete elliptic integral of the third kind for
float
modulus k
.
long double std::comp_ellint_3l | ( | long double | __k, |
long double | __nu | ||
) | [inline] |
Return the complete elliptic integral of the third kind for
long double
modulus k
.
__gnu_cxx::__promote_2<_Tpnu, _Tp>::__type std::cyl_bessel_i | ( | _Tpnu | __nu, |
_Tp | __x | ||
) | [inline] |
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 . |
float std::cyl_bessel_if | ( | float | __nu, |
float | __x | ||
) | [inline] |
Return the regular modified Bessel function for
float
order and argument
.
long double std::cyl_bessel_il | ( | long double | __nu, |
long double | __x | ||
) | [inline] |
Return the regular modified Bessel function for
long double
order and argument
.
__gnu_cxx::__promote_2<_Tpnu, _Tp>::__type std::cyl_bessel_j | ( | _Tpnu | __nu, |
_Tp | __x | ||
) | [inline] |
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 . |
float std::cyl_bessel_jf | ( | float | __nu, |
float | __x | ||
) | [inline] |
Return the Bessel function of the first kind for
float
order and argument
.
long double std::cyl_bessel_jl | ( | long double | __nu, |
long double | __x | ||
) | [inline] |
Return the Bessel function of the first kind for
long double
order and argument
.
__gnu_cxx::__promote_2<_Tpnu, _Tp>::__type std::cyl_bessel_k | ( | _Tpnu | __nu, |
_Tp | __x | ||
) | [inline] |
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 . |
float std::cyl_bessel_kf | ( | float | __nu, |
float | __x | ||
) | [inline] |
Return the irregular modified Bessel function for
float
order and argument
.
long double std::cyl_bessel_kl | ( | long double | __nu, |
long double | __x | ||
) | [inline] |
Return the irregular modified Bessel function for
long double
order and argument
.
__gnu_cxx::__promote_2<_Tpnu, _Tp>::__type std::cyl_neumann | ( | _Tpnu | __nu, |
_Tp | __x | ||
) | [inline] |
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 . |
float std::cyl_neumannf | ( | float | __nu, |
float | __x | ||
) | [inline] |
Return the Neumann function of
float
order and argument
.
long double std::cyl_neumannl | ( | long double | __nu, |
long double | __x | ||
) | [inline] |
Return the Neumann function of
long double
order and argument
.
__gnu_cxx::__promote_2<_Tp, _Tpp>::__type std::ellint_1 | ( | _Tp | __k, |
_Tpp | __phi | ||
) | [inline] |
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 . |
float std::ellint_1f | ( | float | __k, |
float | __phi | ||
) | [inline] |
long double std::ellint_1l | ( | long double | __k, |
long double | __phi | ||
) | [inline] |
__gnu_cxx::__promote_2<_Tp, _Tpp>::__type std::ellint_2 | ( | _Tp | __k, |
_Tpp | __phi | ||
) | [inline] |
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 . |
float std::ellint_2f | ( | float | __k, |
float | __phi | ||
) | [inline] |
long double std::ellint_2l | ( | long double | __k, |
long double | __phi | ||
) | [inline] |
__gnu_cxx::__promote_3<_Tp, _Tpn, _Tpp>::__type std::ellint_3 | ( | _Tp | __k, |
_Tpn | __nu, | ||
_Tpp | __phi | ||
) | [inline] |
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 . |
float std::ellint_3f | ( | float | __k, |
float | __nu, | ||
float | __phi | ||
) | [inline] |
long double std::ellint_3l | ( | long double | __k, |
long double | __nu, | ||
long double | __phi | ||
) | [inline] |
__gnu_cxx::__promote<_Tp>::__type std::expint | ( | _Tp | __x | ) | [inline] |
float std::expintf | ( | float | __x | ) | [inline] |
long double std::expintl | ( | long double | __x | ) | [inline] |
__gnu_cxx::__promote<_Tp>::__type std::hermite | ( | unsigned int | __n, |
_Tp | __x | ||
) | [inline] |
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 |
float std::hermitef | ( | unsigned int | __n, |
float | __x | ||
) | [inline] |
long double std::hermitel | ( | unsigned int | __n, |
long double | __x | ||
) | [inline] |
__gnu_cxx::__promote<_Tp>::__type std::laguerre | ( | unsigned int | __n, |
_Tp | __x | ||
) | [inline] |
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 . |
float std::laguerref | ( | unsigned int | __n, |
float | __x | ||
) | [inline] |
long double std::laguerrel | ( | unsigned int | __n, |
long double | __x | ||
) | [inline] |
__gnu_cxx::__promote<_Tp>::__type std::legendre | ( | unsigned int | __l, |
_Tp | __x | ||
) | [inline] |
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 |
float std::legendref | ( | unsigned int | __l, |
float | __x | ||
) | [inline] |
long double std::legendrel | ( | unsigned int | __l, |
long double | __x | ||
) | [inline] |
__gnu_cxx::__promote<_Tp>::__type std::riemann_zeta | ( | _Tp | __s | ) | [inline] |
float std::riemann_zetaf | ( | float | __s | ) | [inline] |
Return the Riemann zeta function for
float
argument .
long double std::riemann_zetal | ( | long double | __s | ) | [inline] |
Return the Riemann zeta function for
long double
argument .
__gnu_cxx::__promote<_Tp>::__type std::sph_bessel | ( | unsigned int | __n, |
_Tp | __x | ||
) | [inline] |
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 . |
float std::sph_besself | ( | unsigned int | __n, |
float | __x | ||
) | [inline] |
Return the spherical Bessel function of nonnegative order n and
float
argument .
long double std::sph_bessell | ( | unsigned int | __n, |
long double | __x | ||
) | [inline] |
Return the spherical Bessel function of nonnegative order n and
long double
argument .
__gnu_cxx::__promote<_Tp>::__type std::sph_legendre | ( | unsigned int | __l, |
unsigned int | __m, | ||
_Tp | __theta | ||
) | [inline] |
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 |
float std::sph_legendref | ( | unsigned int | __l, |
unsigned int | __m, | ||
float | __theta | ||
) | [inline] |
Return the spherical Legendre function of nonnegative integral degree l
and order m
and float angle in radians.
long double std::sph_legendrel | ( | unsigned int | __l, |
unsigned int | __m, | ||
long double | __theta | ||
) | [inline] |
Return the spherical Legendre function of nonnegative integral degree l
and order m
and long double
angle in radians.
__gnu_cxx::__promote<_Tp>::__type std::sph_neumann | ( | unsigned int | __n, |
_Tp | __x | ||
) | [inline] |
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 . |
float std::sph_neumannf | ( | unsigned int | __n, |
float | __x | ||
) | [inline] |
Return the spherical Neumann function of integral order and
float
argument .
long double std::sph_neumannl | ( | unsigned int | __n, |
long double | __x | ||
) | [inline] |
Return the spherical Neumann function of integral order and
long double
.