Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.4541)

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=7/2

http://functions.wolfram.com/07.25.03.4541.01

Input Form

HypergeometricPFQ[{-(9/2), 3}, {7/2, 5}, -z] == -((24 (-3 + 17 z))/(2431 z^4)) + (1/(130690560 z^4)) ((-3870720 + 18063360 z - 14460705 z^2 + 19511100 z^3 + 63734580 z^4 + 30053664 z^5 + 5216208 z^6 + 372416 z^7 + 9152 z^8)/E^z) + (1/(261381120 z^(5/2))) (Sqrt[Pi] (34459425 - 32162130 z + 82702620 z^2 + 153153000 z^3 + 64974000 z^4 + 10795680 z^5 + 753984 z^6 + 18304 z^7) 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]