Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9645)

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=-19/4, b_1`>=-11/2

For fixed z and a₁=-19/4, b_1`=11/2

http://functions.wolfram.com/07.22.03.9645.01

Input Form

HypergeometricPFQ[{-(19/4)}, {11/2, -(5/4)}, -z] == ((4 z (17445345080625 + 3033973057500 z + 1076955264000 z^2 + 1570271155200 z^3 - 1431606067200 z^4 + 1187374694400 z^5 + 344360222720 z^6 + 14763950080 z^7 + 134217728 z^8) BesselJ[-(1/4), Sqrt[z]]^2 - 4 Sqrt[z] (52336035241875 - 866849445000 z + 979308792000 z^2 + 1148752281600 z^3 - 873050112000 z^4 + 497693491200 z^5 + 167679098880 z^6 + 7340032000 z^7 + 67108864 z^8) BesselJ[-(1/4), Sqrt[z]] BesselJ[3/4, Sqrt[z]] + (157008105725625 - 32506854187500 z + 1879694586000 z^2 + 2794016332800 z^3 + 7956323020800 z^4 - 6474439065600 z^5 + 4427218944000 z^6 + 1362886656000 z^7 + 58921582592 z^8 + 536870912 z^9) BesselJ[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/ (3756186720000 Sqrt[2] z^(15/4))

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]