Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a7sj)

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`=5/2

http://functions.wolfram.com/07.22.03.a7sj.01

Input Form

HypergeometricPFQ[{-(17/4)}, {5/2, 17/4}, -z] == ((2 Sqrt[z] (-406586755575 - 2168462696400 z + 131914632326400 z^2 + 171946228101120 z^3 + 39786905272320 z^4 + 2500611538944 z^5 + 49375346688 z^6 + 268435456 z^7) BesselJ[1/4, Sqrt[z]]^2 - 3 (-677644592625 - 4095985093200 z + 26985313555200 z^2 + 140520771072000 z^3 + 37670017105920 z^4 + 2457804472320 z^5 + 49140465664 z^6 + 268435456 z^7) BesselJ[1/4, Sqrt[z]] BesselJ[5/4, 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[5/4, Sqrt[z]]^2) Gamma[5/4]^2)/(114616354406400 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]