Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.5142)

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=9/2, b₁>=-11/2

For fixed z and a₁=-9/2, a₂=9/2, b₁=7/2

http://functions.wolfram.com/07.25.03.5142.01

Input Form

HypergeometricPFQ[{-(9/2), 9/2}, {7/2, 11/2}, -z] == (1/(11010048 z^4)) ((99225 + 66150 z - 381780 z^2 + 1005480 z^3 + 6034224 z^4 + 3848736 z^5 + 836160 z^6 + 71552 z^7 + 2048 z^8)/E^z) + (1/(22020096 z^(9/2))) (Sqrt[Pi] (-99225 + 408240 z^2 - 1270080 z^3 + 5715360 z^4 + 15240960 z^5 + 8467200 z^6 + 1741824 z^7 + 145152 z^8 + 4096 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]