Regularized confluent hypergeometric function 0F1: Representations through more general functions (formula 07.18.26.0122)

Hypergeometric0F1Regularized

$Mathematica Notation$

Hypergeometric Functions

Hypergeometric0F1Regularized[b,z]

Representations through more general functions

Through Meijer G

Classical cases involving Bessel I

http://functions.wolfram.com/07.18.26.0122.01

Input Form

Hypergeometric0F1Regularized[b, z] BesselI[b, 2 Sqrt[z]] == 2^(-1 + b) Sqrt[Pi] Csc[(1/4 + b) Pi] MeijerG[{{(1 - b)/2}, {(1/4) (3 - 2 b)}}, {{b/2}, {-(b/2), 1 - (3 b)/2, (1/4) (3 - 2 b)}}, 4 z]

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]