Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.af1z)

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.af1z.01

Input Form

HypergeometricPFQ[{17/4}, {-(11/2), 23/4}, -z] == -((19 (2 Sqrt[z] (8754746870244375 - 9891542108448000 z + 2051730705024000 z^2 - 185890450636800 z^3 + 9086525767680 z^4 - 247883366400 z^5 + 2751463424 z^6) BesselJ[-(1/4), Sqrt[z]]^2 + (-26264240610733125 + 69696326303604000 z - 23098599171648000 z^2 + 2912642056396800 z^3 - 186727455129600 z^4 + 6769323540480 z^5 - 125527130112 z^6 + 536870912 z^7) BesselJ[-(1/4), Sqrt[z]] BesselJ[3/4, Sqrt[z]] - 6 Sqrt[z] (8754746870244375 - 4555315444680000 z + 827514329241600 z^2 - 70720299417600 z^3 + 3335218790400 z^4 - 88101355520 z^5 + 939524096 z^6) BesselJ[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/(58888028160 Sqrt[2] z^(17/4)))

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]