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

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`=-7/2

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

Input Form

HypergeometricPFQ[{11/4}, {-(7/2), 23/4}, z] == (1/(7516192768 z^(19/4))) ((209 (4 z^(1/4) (-17313276605625 - 23084368807500 Sqrt[z] - 17348252922000 z - 9060531480000 z^(3/2) - 3524367974400 z^2 - 1060732108800 z^(5/2) - 251510784000 z^3 - 46792704000 z^(7/2) - 6606028800 z^4 - 645922816 z^(9/2) - 33554432 z^5 + E^(4 Sqrt[z]) (17313276605625 - 23084368807500 Sqrt[z] + 17348252922000 z - 9060531480000 z^(3/2) + 3524367974400 z^2 - 1060732108800 z^(5/2) + 251510784000 z^3 - 46792704000 z^(7/2) + 6606028800 z^4 - 645922816 z^(9/2) + 33554432 z^5)) + 109643625 E^(2 Sqrt[z]) Sqrt[2 Pi] (157905 - 10208 z + 256 z^2) Erf[Sqrt[2] z^(1/4)] - 109643625 E^(2 Sqrt[z]) Sqrt[2 Pi] (157905 - 10208 z + 256 z^2) Erfi[Sqrt[2] z^(1/4)]))/E^(2 Sqrt[z]))

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]