Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.4536)

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=3, b₁>=-11/2

For fixed z and a₁=-9/2, a₂=3, b₁=3

http://functions.wolfram.com/07.25.03.4536.01

Input Form

HypergeometricPFQ[{-(9/2), 3}, {3, 11/2}, -z] == (1/(3145728 z^4)) ((-99225 + 189000 z - 264600 z^2 + 423360 z^3 + 1572864 z^4 + 781440 z^5 + 140160 z^6 + 10240 z^7 + 256 z^8)/E^z) + (1/(6291456 z^(9/2))) (Sqrt[Pi] (99225 - 255150 z + 408240 z^2 - 635040 z^3 + 1905120 z^4 + 3810240 z^5 + 1693440 z^6 + 290304 z^7 + 20736 z^8 + 512 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]