Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9684)

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=-17/4, b_1`>=-11/2

For fixed z and a₁=-17/4, b_1`=-11/2

http://functions.wolfram.com/07.22.03.9684.01

Input Form

HypergeometricPFQ[{-(17/4)}, {-(11/2), -(13/4)}, z] == (1/2432430) ((1216215 + 1216215 E^(4 Sqrt[z]) + 2432430 Sqrt[z] - 2432430 E^(4 Sqrt[z]) Sqrt[z] + 2143260 z + 2143260 E^(4 Sqrt[z]) z + 1043280 z^(3/2) - 1043280 E^(4 Sqrt[z]) z^(3/2) + 278880 z^2 + 278880 E^(4 Sqrt[z]) z^2 + 31584 z^(5/2) - 31584 E^(4 Sqrt[z]) z^(5/2) + 192 z^3 + 192 E^(4 Sqrt[z]) z^3 - 256 z^(7/2) + 256 E^(4 Sqrt[z]) z^(7/2) + 1024 z^4 + 1024 E^(4 Sqrt[z]) z^4 + 1024 E^(2 Sqrt[z]) Sqrt[2 Pi] z^(17/4) Erf[Sqrt[2] z^(1/4)] - 1024 E^(2 Sqrt[z]) Sqrt[2 Pi] z^(17/4) 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]