Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8648)

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=-21/4, b_1`>=-11/2

For fixed z and a₁=-21/4, b_1`=-7/2

http://functions.wolfram.com/07.22.03.8648.01

Input Form

HypergeometricPFQ[{-(21/4)}, {-(7/2), 7/4}, z] == (1/(158544691200 z^(3/4))) ((-4 z^(1/4) (6230890575 - 11510232300 Sqrt[z] + 2196316080 z - 5910287040 z^(3/2) + 474969600 z^2 - 1505064960 z^(5/2) + 85155840 z^3 - 280068096 z^(7/2) + 23789568 z^4 - 98304000 z^(9/2) - 1048576 z^5 + 4194304 z^(11/2) + E^(4 Sqrt[z]) (-6230890575 - 11510232300 Sqrt[z] - 2196316080 z - 5910287040 z^(3/2) - 474969600 z^2 - 1505064960 z^(5/2) - 85155840 z^3 - 280068096 z^(7/2) - 23789568 z^4 - 98304000 z^(9/2) + 1048576 z^5 + 4194304 z^(11/2))) - E^(2 Sqrt[z]) Sqrt[2 Pi] (-6230890575 - 35186205600 z - 21653049600 z^2 - 5702860800 z^3 - 1052835840 z^4 - 396361728 z^5 + 16777216 z^6) Erf[Sqrt[2] z^(1/4)] + E^(2 Sqrt[z]) Sqrt[2 Pi] (-6230890575 - 35186205600 z - 21653049600 z^2 - 5702860800 z^3 - 1052835840 z^4 - 396361728 z^5 + 16777216 z^6) Erfi[Sqrt[2] z^(1/4)])/E^(2 Sqrt[z]))

Standard Form

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MathML 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]