Mathematical special functions

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)

Notes

Overloads for math special functions are present in the final draft of ISO/IEC 29124:2010 (N3060), but absent in C++17/20 standard. These overloads are not provided by some implementations. We intendedly consider the missing of these overloads a defect in C++17/20. See also LWG issue 3234.

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

Feature testing macro: __cpp_lib_math_special_functions.

References

• C++20 standard (ISO/IEC 14882:2020):
• 26.8.6 Mathematical special functions [sf.cmath]
• C++17 standard (ISO/IEC 14882:2017):
• 29.9.5 Mathematical special functions [sf.cmath]