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Part 2 §20: Special Functions II

Additional special functions

30 entries· Edition 2019FR→ About Part 2
2-20Euler-Mascheroni constant
30
2-20.1
Euler-Mascheroni constant γ , C
Euler-Mascheroni constant
2-20.2
gamma function Γ ( z )
gamma function
2-20.3
Riemann zeta function ζ ( z )
Riemann zeta function
2-20.4
beta function B ( z , w )
beta function
2-20.5
exponential integral Ei x
exponential integral
2-20.6
logarithmic integral li x
logarithmic integral
2-20.7
sine integral Si z
sine integral
2-20.8
Fresnel integral S ( z ) , C ( z )
Fresnel integrals
2-20.9
error function erf x
error function
2-20.10
incomplete elliptic integral of the first kind F ( φ , k )
incomplete elliptic integral of the first kind
2-20.11
incomplete elliptic integral of the second kind E ( φ , k )
incomplete elliptic integral of the second kind
2-20.12
incomplete elliptic integral of the third kind Π ( n , φ , k )
incomplete elliptic integral of the third kind
2-20.13
hypergeometric function F ( a , b , c ; z )
hypergeometric function
2-20.14
confluent hypergeometric function F ( a ; c ; z )
confluent hypergeometric function
2-20.15
Legendre polynomial P n ( z )
Legendre polynomial
2-20.16
associated Legendre function P n m ( z )
associated Legendre function
2-20.17
spherical harmonic Y l m ( ϑ , φ )
spherical harmonic
2-20.18
Hermite polynomial H n ( z )
Hermite polynomial
2-20.19
Laguerre polynomial L n ( z )
Laguerre polynomial
2-20.20
associated Laguerre polynomial L n m ( z )
associated Laguerre polynomial
2-20.21
Chebyshev polynomial of the first kind T n ( z )
Chebyshev polynomial of the first kind
2-20.22
Chebyshev polynomial of the second kind U n ( z )
Chebyshev polynomial of the second kind
2-20.23
Bessel function J ν ( z )
Bessel function, + cylinder function of the first kind
2-20.24
Neumann function N ν ( z )
Neumann function, + cylinder Bessel function of the second kind
2-20.25
Hankel function H ν ( 1 ) ( z ) , H ν ( 2 ) ( z )
Hankel function, + cylinder Bessel function of the third kind
2-20.26
modified Bessel function I ν ( z ) , K ν ( z )
modified Bessel function
2-20.27
spherical Bessel function j l ( z )
spherical Bessel function
2-20.28
spherical Neumann function n l ( z )
spherical Neumann function
2-20.29
spherical Hankel function h l ( 1 ) ( z ) , h l ( 2 ) ( z )
spherical Hankel function
2-20.30
Airy function Ai ( z ) , Bi ( z )
Airy function
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