Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9381)

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`=-1/2

http://functions.wolfram.com/07.22.03.9381.01

Input Form

HypergeometricPFQ[{-(19/4)}, {-(1/2), 19/4}, -z] == ((-2 Sqrt[z] (29492271183375 - 12256528284000 z - 3016991577600 z^2 - 42186098073600 z^3 + 97606906675200 z^4 + 135490311290880 z^5 + 17919241093120 z^6 + 564251328512 z^7 + 4294967296 z^8) BesselJ[-(1/4), Sqrt[z]]^2 + (88476813550125 - 171591395976000 z - 48271865241600 z^2 - 10727081164800 z^3 + 37130511974400 z^4 + 125188586864640 z^5 + 17573798215680 z^6 + 561566973952 z^7 + 4294967296 z^8) BesselJ[-(1/4), Sqrt[z]] BesselJ[3/4, Sqrt[z]] - 2 Sqrt[z] (-88476813550125 - 17159139597600 z - 17096285606400 z^2 - 37544784076800 z^3 + 69775412428800 z^4 + 131223005429760 z^5 + 17779855982592 z^6 + 563177586688 z^7 + 4294967296 z^8) BesselJ[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/(97606906675200 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]