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

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=-5/4, b_1`>=-11/2

For fixed z and a₁=-5/4, b_1`=11/2

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

Input Form

HypergeometricPFQ[{-(5/4)}, {11/2, -(7/4)}, -z] == -((1/(1076768 Sqrt[2] z^(13/4))) ((4 z (109643625 + 4455360 z + 562944 z^2 - 663552 z^3 + 65536 z^4) BesselJ[1/4, Sqrt[z]]^2 - 12 Sqrt[z] (182739375 - 8817900 z + 620160 z^2 - 360448 z^3 + 32768 z^4) BesselJ[1/4, Sqrt[z]] BesselJ[5/4, Sqrt[z]] + (2741090625 - 375921000 z + 12729600 z^2 + 4500480 z^3 - 2850816 z^4 + 262144 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]