Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a8f4)

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=-13/4, b_1`>=-11/2

For fixed z and a₁=-13/4, b_1`=-9/2

http://functions.wolfram.com/07.22.03.a8f4.01

Input Form

HypergeometricPFQ[{-(13/4)}, {-(9/2), 15/4}, z] == (11 (4 z^(1/4) (-372020819625 - 496027759500 Sqrt[z] - 220891179600 z + 7819156800 z^(3/2) - 6950361600 z^2 + 24546723840 z^(5/2) - 888053760 z^3 + 3400433664 z^(7/2) - 46989312 z^4 + 184811520 z^(9/2) - 1048576 z^5 + 4194304 z^(11/2) + E^(4 Sqrt[z]) (372020819625 - 496027759500 Sqrt[z] + 220891179600 z + 7819156800 z^(3/2) + 6950361600 z^2 + 24546723840 z^(5/2) + 888053760 z^3 + 3400433664 z^(7/2) + 46989312 z^4 + 184811520 z^(9/2) + 1048576 z^5 + 4194304 z^(11/2))) + E^(2 Sqrt[z]) Sqrt[2 Pi] (372020819625 - 175931028000 z + 93829881600 z^2 + 95319244800 z^3 + 13456834560 z^4 + 736100352 z^5 + 16777216 z^6) Erf[Sqrt[2] z^(1/4)] - E^(2 Sqrt[z]) Sqrt[2 Pi] (372020819625 - 175931028000 z + 93829881600 z^2 + 95319244800 z^3 + 13456834560 z^4 + 736100352 z^5 + 16777216 z^6) Erfi[Sqrt[2] z^(1/4)]))/E^(2 Sqrt[z])/(6957847019520 z^(11/4))

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]