Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a8s8)

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`=11/2

http://functions.wolfram.com/07.22.03.a8s8.01

Input Form

HypergeometricPFQ[{-(13/4)}, {11/2, 7/4}, z] == (1/(2746681344 z^(9/2))) ((-2 (-42567525 - 85135050 Sqrt[z] - 50859900 z + 11793600 z^(3/2) + 13731120 z^2 - 18532800 z^(5/2) + 11232000 z^3 + 62899200 z^(7/2) + 75243870 z^4 - 347547864 z^(9/2) - 18058848 z^5 + 74603904 z^(11/2) + 817664 z^6 - 3295232 z^(13/2) - 8192 z^7 + 32768 z^(15/2) + E^(4 Sqrt[z]) (42567525 - 85135050 Sqrt[z] + 50859900 z + 11793600 z^(3/2) - 13731120 z^2 - 18532800 z^(5/2) - 11232000 z^3 + 62899200 z^(7/2) - 75243870 z^4 - 347547864 z^(9/2) + 18058848 z^5 + 74603904 z^(11/2) - 817664 z^6 - 3295232 z^(13/2) + 8192 z^7 + 32768 z^(15/2))) + E^(2 Sqrt[z]) Sqrt[2 Pi] z^(15/4) (-213974865 + 720757440 z - 150418944 z^2 + 6602752 z^3 - 65536 z^4) Erf[Sqrt[2] z^(1/4)] + E^(2 Sqrt[z]) Sqrt[2 Pi] z^(15/4) (213974865 - 720757440 z + 150418944 z^2 - 6602752 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]