Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.2164)

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=-11/2, a₂>=-11/2

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

For fixed z and a₁=-11/2, a₂=4, b₁=9/2

http://functions.wolfram.com/07.25.03.2164.01

Input Form

HypergeometricPFQ[{-(11/2), 4}, {9/2, 5}, -z] == 168/(4199 z^4) + (1/(37150064640 z^4)) ((-1486356480 + 1787288895 z - 2489122440 z^2 + 4291728840 z^3 + 19528922880 z^4 + 12040423296 z^5 + 2859974016 z^6 + 311645568 z^7 + 15508480 z^8 + 282880 z^9)/E^z) + (1/(74300129280 z^(7/2))) (Sqrt[Pi] (-3273645375 + 3928374450 z - 6285399120 z^2 + 20951330400 z^3 + 48886437600 z^4 + 26665329600 z^5 + 6016792320 z^6 + 638516736 z^7 + 31299840 z^8 + 565760 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]