Regularized confluent hypergeometric function 0F1: Representations through more general functions (formula 07.18.26.0083)

Hypergeometric0F1Regularized

$Mathematica Notation$

Hypergeometric Functions

Hypergeometric0F1Regularized[b,z]

Representations through more general functions

Through Meijer G

Classical cases involving cosh

http://functions.wolfram.com/07.18.26.0083.01

Input Form

Cosh[a + z] Hypergeometric0F1Regularized[b, z^2/4] == (2^(-3 + 2 b)/Sqrt[Pi]) (MeijerG[{{3/2 - b}, {}}, {{0}, {2 - 2 b}}, 2 z]/ E^a + E^a Pi Csc[b Pi] MeijerG[{{3/2 - b}, {1 - b}}, {{0}, {2 - 2 b, 1 - b}}, 2 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]