Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.5283)

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=5, b₁>=-11/2

For fixed z and a₁=-9/2, a₂=5, b₁=1

http://functions.wolfram.com/07.25.03.5283.01

Input Form

HypergeometricPFQ[{-(9/2), 5}, {1, 11/2}, -z] == (1/(402653184 z^4)) ((-3472875 - 3591000 z - 3001320 z^2 - 4596480 z^3 + 333374592 z^4 + 804220032 z^5 + 404866176 z^6 + 65162240 z^7 + 3111680 z^8)/E^z) + (1/(805306368 z^(9/2))) (Sqrt[Pi] (3472875 + 1275750 z + 1224720 z^2 + 3175200 z^3 + 66679200 z^4 + 1200225600 z^5 + 1955923200 z^6 + 871782912 z^7 + 133436160 z^8 + 6223360 z^9) Erf[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},{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]