Confluent hypergeometric function 0F1: Representations through more general functions (formula 07.17.26.0137)

Hypergeometric0F1

$Mathematica Notation$

Hypergeometric Functions

Hypergeometric0F1[b,z]

Representations through more general functions

Through Meijer G

Classical cases involving Bessel Y

http://functions.wolfram.com/07.17.26.0137.01

Input Form

Hypergeometric0F1[b, -(z^2/4)] BesselY[\[Nu], z] == (-((2^(-1 + b) Gamma[b])/Sqrt[Pi])) MeijerG[{{(1 - b)/2, 1 - b/2}, {(1 - \[Nu])/2}}, {{-(\[Nu]/2), \[Nu]/2}, {(1 - \[Nu])/2, 1 - b - \[Nu]/2, 1 - b + \[Nu]/2}}, z^2] /; !(Element[-b - \[Nu], Integers] && -b - \[Nu] >= 0) && !(Element[-b + \[Nu], Integers] && -b + \[Nu] >= 0) && Inequality[-(Pi/2), Less, Arg[z], LessEqual, Pi/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]