Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.an13)

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=9/2, a₂>=9/2

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

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

http://functions.wolfram.com/07.25.03.an13.01

Input Form

HypergeometricPFQ[{9/2, 6}, {-(11/2), 1/2}, -z] == (1/16372125) (16372125 + 160744500 z + 458419500 z^2 + 908107200 z^3 + 1751349600 z^4 + 4410806400 z^5 + 27935107200 z^6 - 60363273600 z^7 + 41336144640 z^8 - 13742006880 z^9 + 2552558400 z^10 - 280926600 z^11 + 18587360 z^12 - 720576 z^13 + 14976 z^14 - 128 z^15) + (1/16372125) ((4 Sqrt[Pi] (-11794280400 z^(13/2) + 19095501600 z^(15/2) - 11802539700 z^(17/2) + 3724509600 z^(19/2) - 671140575 z^(21/2) + 72469530 z^(23/2) - 4735080 z^(25/2) + 182000 z^(27/2) - 3760 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]