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

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=15/4, b_1`>=-11/2

For fixed z and a₁=15/4, b_1`=-5/2

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

Input Form

HypergeometricPFQ[{15/4}, {-(5/2), -(19/4)}, -z] == (1/(228118275 z^(1/4))) (Sqrt[2] ((228118275 + 384199200 z + 38419920 z^2 - 102009600 z^3 - 113541120 z^4 - 317915136 z^5 + 38797312 z^6) BesselJ[1/4, Sqrt[z]]^2 - 4 Sqrt[z] (228118275 + 80041500 z - 126236880 z^2 + 31933440 z^3 - 132464640 z^4 - 92798976 z^5 + 1048576 z^6) BesselJ[1/4, Sqrt[z]] BesselJ[5/4, Sqrt[z]] + 4 z (228118275 - 224116200 z + 114649920 z^2 - 78059520 z^3 + 16465920 z^4 - 8912896 z^5) BesselJ[5/4, Sqrt[z]]^2) Gamma[5/4]^2)

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]