Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.7966)

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=-23/4, b_1`>=-11/2

For fixed z and a₁=-23/4, b_1`=-11/2

http://functions.wolfram.com/07.22.03.7966.01

Input Form

HypergeometricPFQ[{-(23/4)}, {-(11/2), -(3/4)}, z] == (1/383201280) ((4 (47900160 + 95800320 Sqrt[z] + 29030400 z - 69672960 z^(3/2) + 7278705 z^2 - 25045524 z^(5/2) + 962352 z^3 - 3583680 z^(7/2) + 74496 z^4 - 285696 z^(9/2) + 4096 z^5 - 16384 z^(11/2) + E^(4 Sqrt[z]) (47900160 - 95800320 Sqrt[z] + 29030400 z + 69672960 z^(3/2) + 7278705 z^2 + 25045524 z^(5/2) + 962352 z^3 + 3583680 z^(7/2) + 74496 z^4 + 285696 z^(9/2) + 4096 z^5 + 16384 z^(11/2))) - E^(2 Sqrt[z]) Sqrt[2 Pi] z^(7/4) (249843825 + 96909120 z + 14095872 z^2 + 1130496 z^3 + 65536 z^4) Erf[Sqrt[2] z^(1/4)] - E^(2 Sqrt[z]) Sqrt[2 Pi] z^(7/4) (249843825 + 96909120 z + 14095872 z^2 + 1130496 z^3 + 65536 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]