special function

C11532
concept

A special function is a mathematically well-studied function, often arising as a solution to differential equations or integrals, that has established names, properties, and applications across many areas of science and engineering.

All labels observed (26)

Label Occurrences
special function canonical 23
orthogonal polynomials 6
special functions 4

Instances (45)

Instance Via concept surface
Heaviside step function step function
Painlevé transcendents
Weierstrass function pathological function
Weierstrass elliptic functions class of special functions
Gamma function
arithmetic–geometric mean identities special function identity
Jacobi elliptic functions family of special functions
Jacobi polynomials orthogonal polynomials
Fresnel integrals
Dirac delta function generalized function
Riemann–Siegel theta function
Hardy Z-function
Selberg integral special function identity
Lambert W function (later named in his honor)
surface form: Lambert W function
Dirichlet series complex function
Ramanujan theta function q-series
mock theta functions q-series
Zernike
surface form: Zernike polynomials
orthogonal polynomials
Bailey chains concept in basic hypergeometric series
Du Bois-Reymond function continuous function
Dirichlet eta function
Dirichlet kernel trigonometric polynomial
Riemann zeta function
Hamming window tapering function
Hermite
surface form: Hermite polynomials
orthogonal polynomials
Hermite functions special functions
Mittag-Leffler function
Bessel functions
Bessel
surface form: Bessel functions
Gauss hypergeometric function
Beta function
Jacobi theta functions special functions
modular j-invariant classical modular function
Wigner 3j symbols
Brillouin function
Legendre polynomials orthogonal polynomials
Chebyshev polynomials of the first kind orthogonal polynomials
Gegenbauer polynomials family of orthogonal polynomials
Riemann xi function
Langevin function
Barnes G-function
Macdonald polynomials orthogonal polynomials
Möbius transformations
surface form: Möbius transformation
complex function
Hurwitz zeta function
product logarithm