Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.4560)

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=11/2

http://functions.wolfram.com/07.25.03.4560.01

Input Form

HypergeometricPFQ[{-(9/2), 3}, {11/2, 6}, -z] == -((1260 (36 + 342 z + 323 z^2))/(46189 z^5)) + (1/(4540563456 z^5)) ((4459069440 + 23904711495 z + 10395827820 z^2 - 2319226560 z^3 + 1409894640 z^4 + 1708097952 z^5 + 433932096 z^6 + 45828096 z^7 + 2148608 z^8 + 36608 z^9)/E^z) + (1/(9081126912 z^(9/2))) (Sqrt[Pi] (22915517625 + 58925616750 z + 18856197360 z^2 - 4190266080 z^3 + 4190266080 z^4 + 3809332800 z^5 + 911635200 z^6 + 93768192 z^7 + 4333824 z^8 + 73216 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]