Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8221)

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=-23/4, b_1`>=-11/2

For fixed z and a₁=-23/4, b_1`=-1/2

http://functions.wolfram.com/07.22.03.8221.01

Input Form

HypergeometricPFQ[{-(23/4)}, {-(1/2), 11/4}, -z] == -(((2 Sqrt[z] (677644592625 - 13490372610000 z + 62630357587200 z^2 + 153183525580800 z^3 + 38559512985600 z^4 + 2476049694720 z^5 + 49241128960 z^6 + 268435456 z^7) BesselJ[-(1/4), Sqrt[z]]^2 - (2032933777875 + 3614104494000 z + 9619338643200 z^2 + 132711884697600 z^3 + 37091568844800 z^4 + 2445724876800 z^5 + 49073356800 z^6 + 268435456 z^7) BesselJ[-(1/4), Sqrt[z]] BesselJ[3/4, Sqrt[z]] + 2 Sqrt[z] (-2032933777875 - 7951029886800 z + 35668301011200 z^2 + 144425214259200 z^3 + 37959241236480 z^4 + 2463844270080 z^5 + 49174020096 z^6 + 268435456 z^7) BesselJ[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/(31455350784000 Sqrt[2] z^(5/4)))

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]