Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.alz3)

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=4, a₂>=4

For fixed z and a₁=4, a₂=9/2, b₁>=-11/2

For fixed z and a₁=4, a₂=9/2, b₁=-11/2

http://functions.wolfram.com/07.25.03.alz3.01

Input Form

HypergeometricPFQ[{4, 9/2}, {-(11/2), -(1/2)}, -z] == (1/3274425) (3274425 - 21432600 z - 130977000 z^2 - 324324000 z^3 - 681080400 z^4 - 1764322560 z^5 - 11174042880 z^6 + 23442048000 z^7 - 15081050880 z^8 + 4563793920 z^9 - 744311808 z^10 + 68630016 z^11 - 3549440 z^12 + 95232 z^13 - 1024 z^14) + (1/3274425) ((128 Sqrt[Pi] (146512800 z^(13/2) - 229536720 z^(15/2) + 133297920 z^(17/2) - 38325420 z^(19/2) + 6070050 z^(21/2) - 549675 z^(23/2) + 28098 z^(25/2) - 748 z^(27/2) + 8 z^(29/2)) 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]