Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9182)

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=-19/4, b_1`>=-11/2

For fixed z and a₁=-19/4, b_1`=-9/2

http://functions.wolfram.com/07.22.03.9182.01

Input Form

HypergeometricPFQ[{-(19/4)}, {-(9/2), 13/4}, z] == (-4 z^(1/4) (13457837633625 + 17943783511500 Sqrt[z] + 3190005957600 z - 6683822006400 z^(3/2) + 831674269440 z^2 - 2822953835520 z^(5/2) + 113639178240 z^3 - 422311034880 z^(7/2) + 8691056640 z^4 - 33288880128 z^(9/2) + 434110464 z^5 - 1686110208 z^(11/2) + 16777216 z^6 - 67108864 z^(13/2) + E^(4 Sqrt[z]) (13457837633625 - 17943783511500 Sqrt[z] + 3190005957600 z + 6683822006400 z^(3/2) + 831674269440 z^2 + 2822953835520 z^(5/2) + 113639178240 z^3 + 422311034880 z^(7/2) + 8691056640 z^4 + 33288880128 z^(9/2) + 434110464 z^5 + 1686110208 z^(11/2) + 16777216 z^6 + 67108864 z^(13/2))) + E^(2 Sqrt[z]) Sqrt[2 Pi] (13457837633625 - 11165020851600 z + 23300913081600 z^2 + 10901011968000 z^3 + 1661106585600 z^4 + 131790274560 z^5 + 6694109184 z^6 + 268435456 z^7) Erf[Sqrt[2] z^(1/4)] + E^(2 Sqrt[z]) Sqrt[2 Pi] (13457837633625 - 11165020851600 z + 23300913081600 z^2 + 10901011968000 z^3 + 1661106585600 z^4 + 131790274560 z^5 + 6694109184 z^6 + 268435456 z^7) Erfi[Sqrt[2] z^(1/4)])/E^(2 Sqrt[z])/(113644834652160 z^(9/4))

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]