Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a879)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

HypergeometricPFQ[{a₁},{b₁,b₂},z]

Specific values

For rational parameters with larger denominators and fixed z

For fixed z and a₁=-15/4, b_1`>=-11/2

For fixed z and a₁=-15/4, b_1`=3/2

http://functions.wolfram.com/07.22.03.a879.01

Input Form

HypergeometricPFQ[{-(15/4)}, {3/2, 19/4}, -z] == ((2 Sqrt[z] (119401907625 + 8270262000 z + 79394515200 z^2 + 7990319001600 z^3 + 6867483033600 z^4 + 936970813440 z^5 + 32128368640 z^6 + 268435456 z^7) BesselJ[-(1/4), Sqrt[z]]^2 - (358205722875 - 521026506000 z - 185253868800 z^2 + 4940103168000 z^3 + 6332719104000 z^4 + 917341470720 z^5 + 31960596480 z^6 + 268435456 z^7) BesselJ[-(1/4), Sqrt[z]] BesselJ[3/4, Sqrt[z]] + 2 Sqrt[z] (-358205722875 - 243145702800 z - 449902252800 z^2 + 6585313996800 z^3 + 6645296332800 z^4 + 929043578880 z^5 + 32061259776 z^6 + 268435456 z^7) BesselJ[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/ (12200863334400 Sqrt[2] z^(13/4))

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[{},{b},z]
HypergeometricPFQ[{a},{},z]
HypergeometricPFQ[{a},{b},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]