Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.ae73)

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=13/4, b_1`>=-11/2

For fixed z and a₁=13/4, b_1`=-9/2

http://functions.wolfram.com/07.22.03.ae73.01

Input Form

HypergeometricPFQ[{13/4}, {-(9/2), 15/4}, -z] == (1/(66355200 Sqrt[2] z^(9/4))) (11 (2 Sqrt[z] (1059888375 - 1253070000 z + 321719040 z^2 - 45363200 z^3 + 2555904 z^4) BesselJ[-(1/4), Sqrt[z]]^2 + (-3179665125 + 8604414000 z - 3261323520 z^2 + 570961920 z^3 - 54329344 z^4 + 1048576 z^5) BesselJ[-(1/4), Sqrt[z]] BesselJ[3/4, Sqrt[z]] - 2 Sqrt[z] (3179665125 - 1821128400 z + 409893120 z^2 - 52875264 z^3 + 2686976 z^4) BesselJ[3/4, Sqrt[z]]^2) Gamma[3/4]^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]