Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.aen5)

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=15/4, b_1`>=-11/2

For fixed z and a₁=15/4, b_1`=-9/2

http://functions.wolfram.com/07.22.03.aen5.01

Input Form

HypergeometricPFQ[{15/4}, {-(9/2), 17/4}, -z] == (1/(158957568 Sqrt[2] z^(11/4))) (13 (2 Sqrt[z] (11406506265 + 9812048400 z - 3369155328 z^2 + 474845184 z^3 - 45023232 z^4 + 1048576 z^5) BesselJ[1/4, Sqrt[z]]^2 - 3 (19010843775 + 29872236240 z - 14342549760 z^2 + 2450460672 z^3 - 263258112 z^4 + 13631488 z^5) BesselJ[1/4, Sqrt[z]] BesselJ[5/4, Sqrt[z]] - 2 Sqrt[z] (-57032531325 + 32052691440 z - 6811326720 z^2 + 819228672 z^3 - 61145088 z^4 + 1048576 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]