Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a7vn)

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`=11/2

http://functions.wolfram.com/07.22.03.a7vn.01

Input Form

HypergeometricPFQ[{-(17/4)}, {11/2, -(15/4)}, -z] == ((4 z (-208703679809625 - 16864943823000 z - 1224920188800 z^2 + 3339973969920 z^3 - 564701921280 z^4 + 45460488192 z^5 - 2407530496 z^6 + 134217728 z^7) BesselJ[1/4, Sqrt[z]]^2 - 12 Sqrt[z] (-347839466349375 + 2810823970500 z - 2823250248000 z^2 + 1963317888000 z^3 - 304457072640 z^4 + 23882629120 z^5 - 1262485504 z^6 + 67108864 z^7) BesselJ[1/4, Sqrt[z]] BesselJ[5/4, Sqrt[z]] + (-5217591995240625 + 505948314690000 z - 30240588924000 z^2 - 18132424128000 z^3 + 15274983628800 z^4 - 2406287278080 z^5 + 189593026560 z^6 - 10032775168 z^7 + 536870912 z^8) BesselJ[5/4, Sqrt[z]]^2) Gamma[5/4]^2)/(5204746562400 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]