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

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=7/4, b_1`>=-11/2

For fixed z and a₁=7/4, b_1`=-11/2

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

Input Form

HypergeometricPFQ[{7/4}, {-(11/2), 19/4}, z] == (1/(2415919104 z^(15/4))) ((4 z^(1/4) (-42706082293875 - 56941443058500 Sqrt[z] - 42195428074800 z - 21553405473600 z^(3/2) - 8103765196800 z^2 - 2315361484800 z^(5/2) - 508870656000 z^3 - 84994424832 z^(7/2) - 10343153664 z^4 - 830472192 z^(9/2) - 33554432 z^5 + E^(4 Sqrt[z]) (42706082293875 - 56941443058500 Sqrt[z] + 42195428074800 z - 21553405473600 z^(3/2) + 8103765196800 z^2 - 2315361484800 z^(5/2) + 508870656000 z^3 - 84994424832 z^(7/2) + 10343153664 z^4 - 830472192 z^(9/2) + 33554432 z^5)) + 454237875 E^(2 Sqrt[z]) Sqrt[2 Pi] (94017 - 7392 z + 256 z^2) Erf[Sqrt[2] z^(1/4)] - 454237875 E^(2 Sqrt[z]) Sqrt[2 Pi] (94017 - 7392 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]