Regularized confluent hypergeometric function 0F1: Representations through more general functions (formula 07.18.26.0114)

Hypergeometric0F1Regularized

$Mathematica Notation$

Hypergeometric Functions

Hypergeometric0F1Regularized[b,z]

Representations through more general functions

Through Meijer G

Classical cases involving Bessel J

http://functions.wolfram.com/07.18.26.0114.01

Input Form

Hypergeometric0F1Regularized[b, -(z^2/4)] BesselJ[-b, z] == (1/(2 Pi)) ((2^(b + 1) Sin[b Pi])/z^b - 2^b Sqrt[Pi] MeijerG[{{(1 - b)/2, 1 - b/2}, {}}, {{1 - b/2}, {b/2, -(b/2), 1 - (3 b)/2}}, z^2]) /; Inequality[-(Pi/2), Less, Arg[z], LessEqual, Pi/2]

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)

2007-05-02

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