Mathematical special functions

 

C++

Language

Standard Library Headers

Freestanding and hosted implementations

Named requirements

Language support library

Concepts library (C++20)

Diagnostics library

Utilities library

Strings library

Containers library

Iterators library

Ranges library (C++20)

Algorithms library

Numerics library

Input/output library

Localizations library

Regular expressions library (C++11)

Atomic operations library (C++11)

Thread support library (C++11)

Filesystem library (C++17)

Technical Specifications

 

Numerics library

Common mathematical functions

Special mathematical functions

Floating-point environment (C++11)

Complex numbers

Numeric arrays

Pseudo-random number generation

Compile-time rational arithmetic (C++11)

Numeric algorithms

gcd (C++17)

lcm (C++17)

Generic numeric operations

iota (C++11)

accumulate

inner_product

adjacent_difference

partial_sum

reduce (C++17)

transform_reduce (C++17)

inclusive_scan (C++17)

exclusive_scan (C++17)

transform_inclusive_scan (C++17)

transform_exclusive_scan (C++17)

Bit operations

bit_cast (C++20)

ispow2 (C++20)

ceil2 (C++20)

floor2 (C++20)

log2p1 (C++20)

 

Special mathematical functions

assoc_laguerreassoc_laguerrefassoc_laguerrel assoc_legendreassoc_legendrefassoc_legendrel betabetafbetal comp_ellint_1comp_ellint_1fcomp_ellint_1l comp_ellint_2comp_ellint_2fcomp_ellint_2l comp_ellint_3comp_ellint_3fcomp_ellint_3l cyl_bessel_icyl_bessel_ifcyl_bessel_il

cyl_bessel_jcyl_bessel_jfcyl_bessel_jl cyl_bessel_kcyl_bessel_kfcyl_bessel_kl cyl_neumanncyl_neumannfcyl_neumannl ellint_1ellint_1fellint_1l ellint_2ellint_2fellint_2l ellint_3ellint_3fellint_3l expintexpintfexpintl

hermitehermitefhermitel laguerrelaguerreflaguerrel legendrelegendreflegendrel riemann_zetariemann_zetafriemann_zetal sph_besselsph_besselfsph_bessell sph_legendresph_legendrefsph_legendrel sph_neumannsph_neumannfsph_neumannl

 

The Mathematical Special Functions library was originally part of Library TR1 ISO/IEC TR 19768:2007, then published as an independent ISO standard, ISO/IEC 29124:2010, and finally merged to ISO C++ as of C++17.

See Mathematical special functions for the ISO/IEC 29124:2010 version of this library.

Functions

Defined in header <cmath>
assoc_laguerreassoc_laguerrefassoc_laguerrel (C++17)(C++17)(C++17)	associated Laguerre polynomials (function)
assoc_legendreassoc_legendrefassoc_legendrel (C++17)(C++17)(C++17)	associated Legendre polynomials (function)
betabetafbetal (C++17)(C++17)(C++17)	beta function (function)
comp_ellint_1comp_ellint_1fcomp_ellint_1l (C++17)(C++17)(C++17)	(complete) elliptic integral of the first kind (function)
comp_ellint_2comp_ellint_2fcomp_ellint_2l (C++17)(C++17)(C++17)	(complete) elliptic integral of the second kind (function)
comp_ellint_3comp_ellint_3fcomp_ellint_3l (C++17)(C++17)(C++17)	(complete) elliptic integral of the third kind (function)
cyl_bessel_icyl_bessel_ifcyl_bessel_il (C++17)(C++17)(C++17)	regular modified cylindrical Bessel functions (function)
cyl_bessel_jcyl_bessel_jfcyl_bessel_jl (C++17)(C++17)(C++17)	cylindrical Bessel functions (of the first kind) (function)
cyl_bessel_kcyl_bessel_kfcyl_bessel_kl (C++17)(C++17)(C++17)	irregular modified cylindrical Bessel functions (function)
cyl_neumanncyl_neumannfcyl_neumannl (C++17)(C++17)(C++17)	cylindrical Neumann functions (function)
ellint_1ellint_1fellint_1l (C++17)(C++17)(C++17)	(incomplete) elliptic integral of the first kind (function)
ellint_2ellint_2fellint_2l (C++17)(C++17)(C++17)	(incomplete) elliptic integral of the second kind (function)
ellint_3ellint_3fellint_3l (C++17)(C++17)(C++17)	(incomplete) elliptic integral of the third kind (function)
expintexpintfexpintl (C++17)(C++17)(C++17)	exponential integral (function)
hermitehermitefhermitel (C++17)(C++17)(C++17)	Hermite polynomials (function)
legendrelegendreflegendrel (C++17)(C++17)(C++17)	Legendre polynomials (function)
laguerrelaguerreflaguerrel (C++17)(C++17)(C++17)	Laguerre polynomials (function)
riemann_zetariemann_zetafriemann_zetal (C++17)(C++17)(C++17)	Riemann zeta function (function)
sph_besselsph_besselfsph_bessell (C++17)(C++17)(C++17)	spherical Bessel functions (of the first kind) (function)
sph_legendresph_legendrefsph_legendrel (C++17)(C++17)(C++17)	spherical associated Legendre functions (function)
sph_neumannsph_neumannfsph_neumannl (C++17)(C++17)(C++17)	spherical Neumann functions (function)