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

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`=-9/2

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

Input Form

HypergeometricPFQ[{19/4}, {-(9/2), 5/4}, -z] == (1/(3274425 z^(1/4))) (Sqrt[2] ((3274425 + 6548850 z + 2772000 z^2 - 709632 z^3 - 268800 z^4 + 8192 z^5) BesselJ[1/4, Sqrt[z]]^2 + 51 Sqrt[z] (-121275 + 147840 z^2 + 34048 z^3 + 4096 z^4) BesselJ[1/4, Sqrt[z]] BesselJ[5/4, Sqrt[z]] - 2 z (363825 + 3880800 z + 332640 z^2 - 59136 z^3 + 4096 z^4) 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]