Mathematical special functions (since C++17)

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_laguerre assoc_laguerref assoc_laguerrel (C++17) (C++17) (C++17)	associated Laguerre polynomials (function)
assoc_legendre assoc_legendref assoc_legendrel (C++17) (C++17) (C++17)	associated Legendre polynomials (function)
beta betaf betal (C++17) (C++17) (C++17)	beta function (function)
comp_ellint_1 comp_ellint_1f comp_ellint_1l (C++17) (C++17) (C++17)	(complete) elliptic integral of the first kind (function)
comp_ellint_2 comp_ellint_2f comp_ellint_2l (C++17) (C++17) (C++17)	(complete) elliptic integral of the second kind (function)
comp_ellint_3 comp_ellint_3f comp_ellint_3l (C++17) (C++17) (C++17)	(complete) elliptic integral of the third kind (function)
cyl_bessel_i cyl_bessel_if cyl_bessel_il (C++17) (C++17) (C++17)	regular modified cylindrical Bessel functions (function)
cyl_bessel_j cyl_bessel_jf cyl_bessel_jl (C++17) (C++17) (C++17)	cylindrical Bessel functions (of the first kind) (function)
cyl_bessel_k cyl_bessel_kf cyl_bessel_kl (C++17) (C++17) (C++17)	irregular modified cylindrical Bessel functions (function)
cyl_neumann cyl_neumannf cyl_neumannl (C++17) (C++17) (C++17)	cylindrical Neumann functions (function)
ellint_1 ellint_1f ellint_1l (C++17) (C++17) (C++17)	(incomplete) elliptic integral of the first kind (function)
ellint_2 ellint_2f ellint_2l (C++17) (C++17) (C++17)	(incomplete) elliptic integral of the second kind (function)
ellint_3 ellint_3f ellint_3l (C++17) (C++17) (C++17)	(incomplete) elliptic integral of the third kind (function)
expint expintf expintl (C++17) (C++17) (C++17)	exponential integral (function)
hermite hermitef hermitel (C++17) (C++17) (C++17)	Hermite polynomials (function)
legendre legendref legendrel (C++17) (C++17) (C++17)	Legendre polynomials (function)
laguerre laguerref laguerrel (C++17) (C++17) (C++17)	Laguerre polynomials (function)
riemann_zeta riemann_zetaf riemann_zetal (C++17) (C++17) (C++17)	Riemann zeta function (function)
sph_bessel sph_besself sph_bessell (C++17) (C++17) (C++17)	spherical Bessel functions (of the first kind) (function)
sph_legendre sph_legendref sph_legendrel (C++17) (C++17) (C++17)	spherical associated Legendre functions (function)
sph_neumann sph_neumannf sph_neumannl (C++17) (C++17) (C++17)	spherical Neumann functions (function)

Notes

The float and long double overloads for math special functions without the " f " or " l " suffix are present in the final draft of ISO/IEC 29124:2010 ( N3060 ), but absent in the published C++17/20 standard (see LWG issue 3234 ). These overloads were not provided by MSVC STL until VS 2022 17.3.

These functions are unrelated to special member functions of class types.

Feature-test macro	Value	Std	Feature
__cpp_lib_math_special_functions	201603L	(C++17)	Mathematical special functions

Defect reports

The following behavior-changing defect reports were applied retroactively to previously published C++ standards.

DR	Applied to	Behavior as published	Correct behavior
LWG 3234 ( P1467R9 )	C++17	additional overloads for math special functions were missing	these overloads are required

References