Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.4868)

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=4, b₁>=-11/2

For fixed z and a₁=-9/2, a₂=4, b₁=1/2

http://functions.wolfram.com/07.25.03.4868.01

Input Form

HypergeometricPFQ[{-(9/2), 4}, {1/2, 5}, -z] == 168/(2431 z^4) + (1/(291720 z^4)) ((-20160 - 20160 z - 10080 z^2 - 3360 z^3 + 290880 z^4 + 1115661 z^5 + 652806 z^6 + 113828 z^7 + 5720 z^8)/E^z) + (1/583440) (Sqrt[Pi] (1276275 Sqrt[z] + 2784600 z^(3/2) + 1413720 z^(5/2) + 233376 z^(7/2) + 11440 z^(9/2)) 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]