Confluent hypergeometric function 0F1: Representations through more general functions (formula 07.17.26.0085)

Hypergeometric0F1

$Mathematica Notation$

Hypergeometric Functions

Hypergeometric0F1[b,z]

Representations through more general functions

Through Meijer G

Classical cases involving sinh

http://functions.wolfram.com/07.17.26.0085.01

Input Form

Sinh[a + z] Hypergeometric0F1[b, z^2/4] == ((2^(-3 + 2 b) Gamma[b])/Sqrt[Pi]) ((-E^(-a)) MeijerG[{{3/2 - b}, {}}, {{0}, {2 - 2 b}}, 2 z] + 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

HypergeometricPFQ[{},{},z]
HypergeometricPFQ[{a},{},z]
HypergeometricPFQ[{a},{b},z]
HypergeometricPFQ[{a₁},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂},{b₁},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅},{b₁,b₂,b₃,b₄},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅,a₆},{b₁,b₂,b₃,b₄,b₅},z]
HypergeometricPFQ[{a₁,...,a_p},{b₁,...,b_q},z]