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

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

For fixed z and a₁=11/4, b_1`=-1/2

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

Input Form

HypergeometricPFQ[{11/4}, {-(1/2), -(19/4)}, -z] == -((1/(1382535 z^(1/4))) (Sqrt[2] ((-1382535 - 1164240 z + 3880800 z^2 + 5322240 z^3 + 761856 z^4 + 131072 z^5) BesselJ[1/4, Sqrt[z]]^2 + 4 Sqrt[z] (1382535 - 679140 z - 3326400 z^2 + 660480 z^3 + 311296 z^4) BesselJ[1/4, Sqrt[z]] BesselJ[5/4, Sqrt[z]] - 4 z (1382535 - 2522520 z + 1511040 z^2 + 399360 z^3 + 32768 z^4) 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]