Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.6276)

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=1, b₁>=-23/4

For fixed z and a₁=1, b₁=-19/4

http://functions.wolfram.com/07.22.03.6276.01

Input Form

HypergeometricPFQ[{1}, {-(19/4), 23/4}, z] == (1/(2048 z^(19/4))) ((-16 E^(2 Sqrt[z]) z^(3/4) (218243025 + 39382200 z + 2723760 z^2 + 44928 z^3 + 128 z^4) - E^(4 Sqrt[z]) Sqrt[2 Pi] (654729075 - 1309458150 Sqrt[z] + 1240539300 z - 735134400 z^(3/2) + 302702400 z^2 - 90810720 z^(5/2) + 20180160 z^3 - 3294720 z^(7/2) + 380160 z^4 - 28160 z^(9/2) + 1024 z^5) Erf[Sqrt[2] z^(1/4)] + Sqrt[2 Pi] (654729075 + 1309458150 Sqrt[z] + 1240539300 z + 735134400 z^(3/2) + 302702400 z^2 + 90810720 z^(5/2) + 20180160 z^3 + 3294720 z^(7/2) + 380160 z^4 + 28160 z^(9/2) + 1024 z^5) 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]