Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.7704)

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=-7/2, a₂>=-7/2

For fixed z and a₁=-7/2, a₂=4, b₁>=-11/2

For fixed z and a₁=-7/2, a₂=4, b₁=11/2

http://functions.wolfram.com/07.25.03.7704.01

Input Form

HypergeometricPFQ[{-(7/2), 4}, {11/2, 6}, -z] == (840 (4 + 17 z))/(2431 z^5) + (1/(79659008 z^5)) ((-110100480 - 176000895 z + 51346470 z^2 - 26668180 z^3 + 21568680 z^4 + 31122736 z^5 + 7675424 z^6 + 661056 z^7 + 18304 z^8)/E^z) + (1/(159318016 z^(9/2))) (Sqrt[Pi] (-402026625 - 306306000 z + 85765680 z^2 - 49008960 z^3 + 68068000 z^4 + 69305600 z^5 + 15993600 z^6 + 1340416 z^7 + 36608 z^8) 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]