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

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=1/2, a₂>=1/2

For fixed z and a₁=1/2, a₂=4, b₁>=-11/2

For fixed z and a₁=1/2, a₂=4, b₁=-9/2

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

Input Form

HypergeometricPFQ[{1/2, 4}, {-(9/2), -(5/2)}, -z] == (1/42525) (42525 - 7560 z + 5400 z^2 - 21600 z^3 - 176400 z^4 - 1693440 z^5 + 4811904 z^6 - 3285120 z^7 + 895200 z^8 - 111456 z^9 + 6272 z^10 - 128 z^11) + (1/42525) ((16 Sqrt[Pi] (198900 z^(11/2) - 382500 z^(13/2) + 230265 z^(15/2) - 59247 z^(17/2) + 7158 z^(19/2) - 396 z^(21/2) + 8 z^(23/2)) 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]