Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.agd5)

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=23/4, b_1`>=-11/2

For fixed z and a₁=23/4, b_1`=-11/2

http://functions.wolfram.com/07.22.03.agd5.01

Input Form

HypergeometricPFQ[{23/4}, {-(11/2), -(7/4)}, -z] == (1/(14371451325 z^(1/4))) (Sqrt[2] (3 (4790483775 + 6719120100 z + 331808400 z^2 + 10744272000 z^3 + 16980606720 z^4 + 4660432896 z^5 + 3758424064 z^6 - 51380224 z^7) BesselJ[1/4, Sqrt[z]]^2 + 4 Sqrt[z] (-14371451325 - 995425200 z + 3981700800 z^2 - 19798732800 z^3 + 10553034240 z^4 + 7088136192 z^5 - 956694528 z^6 + 2097152 z^7) BesselJ[1/4, Sqrt[z]] BesselJ[5/4, Sqrt[z]] + 12 z (4790483775 - 6055503300 z + 5530140000 z^2 - 5066107200 z^3 - 2429844480 z^4 - 709607424 z^5 + 12320768 z^6) 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]