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

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`=-11/2

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

Input Form

HypergeometricPFQ[{11/4}, {-(11/2), 15/4}, z] == (1/(495452160 z^(11/4))) ((4 z^(1/4) (-104928949125 - 139905265500 Sqrt[z] - 111924212400 z - 63956692800 z^(3/2) - 28425196800 z^2 - 10274503680 z^(5/2) - 3056578560 z^3 - 732512256 z^(7/2) - 133496832 z^4 - 16515072 z^(9/2) - 1048576 z^5 + E^(4 Sqrt[z]) (104928949125 - 139905265500 Sqrt[z] + 111924212400 z - 63956692800 z^(3/2) + 28425196800 z^2 - 10274503680 z^(5/2) + 3056578560 z^3 - 732512256 z^(7/2) + 133496832 z^4 - 16515072 z^(9/2) + 1048576 z^5)) + 104928949125 E^(2 Sqrt[z]) Sqrt[2 Pi] Erf[Sqrt[2] z^(1/4)] - 104928949125 E^(2 Sqrt[z]) Sqrt[2 Pi] 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]