Regularized confluent hypergeometric function 0F1: Representations through more general functions (formula 07.18.26.0087)

Hypergeometric0F1Regularized

$Mathematica Notation$

Hypergeometric Functions

Hypergeometric0F1Regularized[b,z]

Representations through more general functions

Through Meijer G

Classical cases involving Ai^'

http://functions.wolfram.com/07.18.26.0087.01

Input Form

AiryAiPrime[3^(2/3) z^(1/3)] Hypergeometric0F1Regularized[b, z] == (-(1/Pi^(3/2))) 2^(-(8/3) + b) 3^(1/6) MeijerG[{{(1/6) (5 - 3 b), (1/6) (8 - 3 b)}, {}}, {{0, 2/3}, {1 - b, 5/3 - 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)

2003-08-21

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