Regularized confluent hypergeometric function 0F1: Representations through more general functions (formula 07.18.26.0048)

Hypergeometric0F1Regularized

$Mathematica Notation$

Hypergeometric Functions

Hypergeometric0F1Regularized[b,z]

Representations through more general functions

Through Meijer G

Classical cases involving Bessel K

http://functions.wolfram.com/07.18.26.0048.01

Input Form

Hypergeometric0F1Regularized[b, z] BesselK[\[Nu], 2 Sqrt[z]] == (2^(-2 + b)/Sqrt[Pi]) MeijerG[{{(1 - b)/2, 1 - b/2}, {}}, {{-(\[Nu]/2), \[Nu]/2}, {1 - b - \[Nu]/2, 1 - b + \[Nu]/2}}, 4 z] /; !(Element[-b - \[Nu], Integers] && -b - \[Nu] >= 0) && !(Element[-b + \[Nu], Integers] && -b + \[Nu] >= 0)

Standard Form

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MathML Form

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Rule Form

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Date Added to functions.wolfram.com (modification date)

2001-10-29

HypergeometricPFQRegularized[{a},{b},z]
HypergeometricPFQRegularized[{a₁,a₂},{b₁},z]
HypergeometricPFQRegularized[{a₁,...,a_p},{b₁,...,b_q},z]