Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.7404)

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/07.22.03.7404.01

Input Form

HypergeometricPFQ[{5}, {-(21/4), 9/4}, z] == (1/(256628736 z^(5/4))) ((8 E^(2 Sqrt[z]) z^(1/4) (-31216185 - 52445232 z - 3229440 z^2 + 3895296 z^3 - 198144 z^4 + 8192 z^5) + E^(4 Sqrt[z]) Sqrt[2 Pi] (31216185 - 62432370 Sqrt[z] + 134469720 z - 185696280 z^(3/2) + 123409440 z^2 - 21422016 z^(5/2) - 22057728 z^3 + 15109248 z^(7/2) - 2629632 z^4 - 733184 z^(9/2) + 262144 z^5 + 32768 z^(11/2)) Erf[Sqrt[2] z^(1/4)] + Sqrt[2 Pi] (31216185 + 62432370 Sqrt[z] + 134469720 z + 185696280 z^(3/2) + 123409440 z^2 + 21422016 z^(5/2) - 22057728 z^3 - 15109248 z^(7/2) - 2629632 z^4 + 733184 z^(9/2) + 262144 z^5 - 32768 z^(11/2)) 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]