Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a9og)

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=-9/4, b_1`>=-11/2

For fixed z and a₁=-9/4, b_1`=11/2

http://functions.wolfram.com/07.22.03.a9og.01

Input Form

HypergeometricPFQ[{-(9/4)}, {11/2, 15/4}, z] == (1/(41240494080 z^(9/2))) ((7 (4 (108864000 + 217728000 Sqrt[z] - 62208000 z - 414720000 z^(3/2) + 64757475 z^2 - 466616700 z^(5/2) + 34093440 z^3 - 293656320 z^(7/2) - 67115520 z^4 + 282531840 z^(9/2) + 4915200 z^5 - 19857408 z^(11/2) - 65536 z^6 + 262144 z^(13/2) + E^(4 Sqrt[z]) (-108864000 + 217728000 Sqrt[z] + 62208000 z - 414720000 z^(3/2) - 64757475 z^2 - 466616700 z^(5/2) - 34093440 z^3 - 293656320 z^(7/2) + 67115520 z^4 + 282531840 z^(9/2) - 4915200 z^5 - 19857408 z^(11/2) + 65536 z^6 + 262144 z^(13/2))) + E^(2 Sqrt[z]) Sqrt[2 Pi] z^(7/4) (-1839759075 - 1911438000 z - 1359244800 z^2 + 1144627200 z^3 - 79626240 z^4 + 1048576 z^5) Erf[Sqrt[2] z^(1/4)] + E^(2 Sqrt[z]) Sqrt[2 Pi] z^(7/4) (1839759075 + 1911438000 z + 1359244800 z^2 - 1144627200 z^3 + 79626240 z^4 - 1048576 z^5) 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]