Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.7104)

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=4, b₁>=-23/4

For fixed z and a₁=4, b₁=-21/4

http://functions.wolfram.com/07.22.03.7104.01

Input Form

HypergeometricPFQ[{4}, {-(21/4), -(11/4)}, z] == (1/144729585) ((E^(2 Sqrt[z]) (144729585 + 40098240 z + 13478400 z^2 + 11059200 z^3 + 38086656 z^4 - 14622720 z^5 - 131072 z^6) - 256 E^(4 Sqrt[z]) Sqrt[2 Pi] z^(15/4) (35397 - 70794 Sqrt[z] + 32292 z + 29808 z^(3/2) + 5184 z^2 + 256 z^(5/2)) Erf[Sqrt[2] z^(1/4)] + 256 Sqrt[2 Pi] z^(15/4) (-35397 - 70794 Sqrt[z] - 32292 z + 29808 z^(3/2) - 5184 z^2 + 256 z^(5/2)) 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]