Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9513)

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`=5/2

http://functions.wolfram.com/07.22.03.9513.01

Input Form

HypergeometricPFQ[{-(19/4)}, {5/2, 7/4}, -z] == ((2 z (228732047775 + 382412091600 z + 104565772800 z^2 + 7610736640 z^3 + 171376640 z^4 + 1048576 z^5) BesselJ[-(1/4), Sqrt[z]]^2 - Sqrt[z] (99978018525 + 328012146000 z + 100084723200 z^2 + 7505387520 z^3 + 170721280 z^4 + 1048576 z^5) BesselJ[-(1/4), Sqrt[z]] BesselJ[3/4, Sqrt[z]] + 2 (-5474838600 + 162814234275 z + 358947666000 z^2 + 102728102400 z^3 + 7568302080 z^4 + 171114496 z^5 + 1048576 z^6) BesselJ[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/ (385945560000 Sqrt[2] z^(3/4))

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]