Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.7400)

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=5, b₁>=-23/4

For fixed z and a₁=5, b₁=-21/4

http://functions.wolfram.com/07.22.03.7400.01

Input Form

HypergeometricPFQ[{5}, {-(21/4), 1/4}, z] == (1/20049120) ((8 E^(2 Sqrt[z]) (2506140 + 11190825 z - 1455480 z^2 - 931440 z^3 + 151424 z^4 + 2048 z^5) + E^(4 Sqrt[z]) Sqrt[2 Pi] z^(3/4) (-20738025 + 41476050 Sqrt[z] - 26334000 z - 2633400 z^(3/2) + 11149200 z^2 - 4040160 z^(5/2) - 904704 z^3 + 642048 z^(7/2) + 151552 z^4 + 8192 z^(9/2)) Erf[Sqrt[2] z^(1/4)] - Sqrt[2 Pi] z^(3/4) (20738025 + 41476050 Sqrt[z] + 26334000 z - 2633400 z^(3/2) - 11149200 z^2 - 4040160 z^(5/2) + 904704 z^3 + 642048 z^(7/2) - 151552 z^4 + 8192 z^(9/2)) 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]