Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.7838)

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=6, b₁>=-23/4

For fixed z and a₁=6, b₁=-5/4

http://functions.wolfram.com/07.22.03.7838.01

Input Form

HypergeometricPFQ[{6}, {-(5/4), 9/4}, z] == (1/(1966080 z^(5/4))) ((24 E^(2 Sqrt[z]) z^(1/4) (-17325 - 56680 z + 107776 z^2 + 12288 z^3) + E^(4 Sqrt[z]) Sqrt[2 Pi] (51975 - 103950 Sqrt[z] + 498960 z - 859320 z^(3/2) - 184800 z^2 + 1478400 z^(5/2) + 844800 z^3 + 149504 z^(7/2) + 8192 z^4) Erf[Sqrt[2] z^(1/4)] + Sqrt[2 Pi] (51975 + 103950 Sqrt[z] + 498960 z + 859320 z^(3/2) - 184800 z^2 - 1478400 z^(5/2) + 844800 z^3 - 149504 z^(7/2) + 8192 z^4) 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]