Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.aam1)

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=-3/4, b_1`>=-11/2

For fixed z and a₁=-3/4, b_1`=-11/2

http://functions.wolfram.com/07.22.03.aam1.01

Input Form

HypergeometricPFQ[{-(3/4)}, {-(11/2), 23/4}, -z] == -((19 (2 Sqrt[z] (7579867420125 - 7578106707600 z + 746438284800 z^2 - 18113372160 z^3 - 431685632 z^4 + 19922944 z^5) BesselJ[-(1/4), Sqrt[z]]^2 - (22739602260375 - 57385142614800 z + 12401507289600 z^2 - 569389916160 z^3 + 4161208320 z^4 + 19922944 z^5) BesselJ[-(1/4), Sqrt[z]] BesselJ[3/4, Sqrt[z]] + 2 Sqrt[z] (-22739602260375 + 8873991126000 z - 862501685760 z^2 + 15084380160 z^3 - 512163840 z^4 + 19922944 z^5) BesselJ[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/(9663676416 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]