Regularized confluent hypergeometric function 0F1: Representations through more general functions (formula 07.18.26.0112)

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/07.18.26.0112.01

Input Form

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