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Special functions

Table of contents

Elementary special functions

Exponentials

Hyperbolic functions

Inverse hyperbolic functions

Logarithms

Trigonometry

Dirichlet function

Double exponential function

Exponential function

Gudermannian function

Kronecker delta

Logarithm

Ptolemy's table of chords

Sigmoid function

Soboleva modified hyperbolic tangent

Elliptic functions

Elliptic curves

Inverse Jacobi elliptic functions

Inverse lemniscate functions

Abel elliptic functions

Carlson symmetric form

Complex multiplication

Dedekind eta function

Dixon elliptic functions

Elliptic function

Elliptic integral

Equianharmonic

Fundamenta nova theoriae functionum ellipticarum

Fundamental pair of periods

Half-period ratio

J-invariant

Jacobi theta functions (notational variations)

Landen's transformation

Legendre's relation

Lemniscate elliptic functions

Modular lambda function

Nome (mathematics)

Picard–Fuchs equation

Quarter period

Theta function

Weierstrass elliptic function

Weierstrass functions

Hypergeometric functions

Appell series

Bilateral hypergeometric series

Dougall's formula

Elliptic hypergeometric series

Frobenius solution to the hypergeometric equation

General hypergeometric function

Horn function

Humbert series

Hypergeometric function of a matrix argument

Kampé de Fériet function

Lauricella hypergeometric series

Legendre function

List of hypergeometric identities

MacRobert E function

Meijer G-function

Riemann's differential equation

Schwarz's list

Special hypergeometric functions

Bessel function

Bessel–Clifford function

Coulomb wave function

Cunningham function

Error function

Incomplete Bessel functions

Kelvin functions

Lentz's algorithm

Logarithmic integral function

Solid harmonics

Sonine formula

Spherical harmonics

Table of spherical harmonics

Toronto function

Zonal spherical harmonics

Theta functions

Jacobi form

Metaplectic group

Schottky problem

Theta characteristic

Theta divisor

Theta function of a lattice

Zeta and L-functions

Airy zeta function

Apéry's theorem

Arakawa–Kaneko zeta function

Arithmetic zeta function

Artin L-function

Artin conductor

Artin–Mazur zeta function

Automorphic L-function

Barnes zeta function

Basel problem

Beurling zeta function

Birch and Swinnerton-Dyer conjecture

Brumer–Stark conjecture

Chowla–Mordell theorem

Clausen function

Dedekind zeta function

 Ancestors (4)

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