Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a7v7)

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=-17/4, b_1`>=-11/2

For fixed z and a₁=-17/4, b_1`=9/2

http://functions.wolfram.com/07.22.03.a7v7.01

Input Form

HypergeometricPFQ[{-(17/4)}, {9/2, 17/4}, -z] == ((2 Sqrt[z] (113437704805425 - 251209208250000 z + 950666883344640 z^2 + 821124280627200 z^3 + 115218883215360 z^4 + 4771260923904 z^5 + 66488107008 z^6 + 268435456 z^7) BesselJ[1/4, Sqrt[z]]^2 - 3 (189062841342375 - 366807622381200 z + 375439019155200 z^2 + 726936471613440 z^3 + 111140444897280 z^4 + 4713480192000 z^5 + 66253225984 z^6 + 268435456 z^7) BesselJ[1/4, Sqrt[z]] BesselJ[5/4, Sqrt[z]] + 2 Sqrt[z] (257549914747125 - 411308248150800 z + 435357933753600 z^2 + 739212864860160 z^3 + 111705077514240 z^4 + 4721659084800 z^5 + 66286780416 z^6 + 268435456 z^7) BesselJ[5/4, Sqrt[z]]^2) Gamma[5/4]^2)/(685242061701120 Sqrt[2] z^(11/4))

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]