Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.4557)

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=5

http://functions.wolfram.com/07.25.03.4557.01

Input Form

HypergeometricPFQ[{-(9/2), 3}, {5, 11/2}, -z] == -((504 (9 + 17 z))/(2431 z^4)) + (1/(2389770240 z^4)) ((3252989565 + 2773658160 z - 834253560 z^2 + 617228640 z^3 + 971129280 z^4 + 294753792 z^5 + 36071808 z^6 + 1920512 z^7 + 36608 z^8)/ E^z) + (1/(4779540480 z^(9/2))) (Sqrt[Pi] (1206079875 + 9304044750 z + 4962157200 z^2 - 1543782240 z^3 + 1984862880 z^4 + 2205403200 z^5 + 623750400 z^6 + 74027520 z^7 + 3877632 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]