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

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=19/4, b_1`>=-11/2

For fixed z and a₁=19/4, b_1`=-11/2

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

Input Form

HypergeometricPFQ[{19/4}, {-(11/2), -(19/4)}, z] == -((1/(2371289468625 z^(1/4))) (Sqrt[2] ((-2371289468625 + 4311435397500 z - 792026650800 z^2 - 910482249600 z^3 - 261755746560 z^4 - 57167953920 z^5 + 162136719360 z^6 + 151825416192 z^7 + 2332033024 z^8) BesselI[1/4, Sqrt[z]]^2 + 4 Sqrt[z] (-2371289468625 + 1149716106000 z + 1343160403200 z^2 + 442411200000 z^3 + 93942858240 z^4 + 11921817600 z^5 + 109483130880 z^6 + 13539213312 z^7 + 33554432 z^8) BesselI[1/4, Sqrt[z]] BesselI[5/4, Sqrt[z]] + 4 z (-2371289468625 - 2012003185500 z - 737278264800 z^2 - 175637246400 z^3 - 40718684160 z^4 - 21459271680 z^5 + 28217180160 z^6 + 557842432 z^7) BesselI[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]