Confluent hypergeometric function 0F1: Representations through more general functions (formula 07.17.26.0199)

Hypergeometric0F1

$Mathematica Notation$

Hypergeometric Functions

Hypergeometric0F1[b,z]

Representations through more general functions

Through Meijer G

Generalized cases involving Bessel Y

http://functions.wolfram.com/07.17.26.0199.01

Input Form

Hypergeometric0F1[b, -(z^2/4)] BesselY[-b, z] == -((2^b Cot[b Pi])/(z^b Gamma[1 - b])) + ((2^(-1 + b) Gamma[b])/Sqrt[Pi]) MeijerG[{{(1 - b)/2, 1 - b/2}, {(1 + b)/2}}, {{1 - b/2, b/2}, {1 - (3 b)/2, -(b/2), (1 + b)/2}}, z, 1/2]

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

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]