Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.ansh)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

HypergeometricPFQ[{a₁,a₂},{b₁,b₂},z]

Specific values

For integer and half-integer parameters and fixed z

For fixed z and a₁=11/2, a₂>=11/2

For fixed z and a₁=11/2, a₂=6, b₁>=-11/2

For fixed z and a₁=11/2, a₂=6, b₁=-9/2

http://functions.wolfram.com/07.25.03.ansh.01

Input Form

HypergeometricPFQ[{11/2, 6}, {-(9/2), 1/2}, -z] == (1/13395375) (13395375 + 196465500 z + 851350500 z^2 + 2724321600 z^3 + 9924314400 z^4 + 83805321600 z^5 - 266653296000 z^6 + 254932272000 z^7 - 116272558080 z^8 + 29568581280 z^9 - 4505281200 z^10 + 424164360 z^11 - 24687840 z^12 + 858816 z^13 - 16256 z^14 + 128 z^15) - (1/13395375) ((4 Sqrt[Pi] (39997994400 z^(11/2) - 89739090000 z^(13/2) + 75600604800 z^(15/2) - 32309304300 z^(17/2) + 7909092450 z^(19/2) - 1176505155 z^(21/2) + 109024650 z^(23/2) - 6277320 z^(25/2) + 216720 z^(27/2) - 4080 z^(29/2) + 32 z^(31/2)) Erfi[Sqrt[z]])/E^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},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂},{b₁},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]