Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.akb8)

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=3, a₂>=3

For fixed z and a₁=3, a₂=9/2, b₁>=-11/2

For fixed z and a₁=3, a₂=9/2, b₁=-11/2

http://functions.wolfram.com/07.25.03.akb8.01

Input Form

HypergeometricPFQ[{3, 9/2}, {-(11/2), -(3/2)}, -z] == (1/3274425) (3274425 - 5358150 z + 26195400 z^2 + 162162000 z^3 + 486486000 z^4 + 1543782240 z^5 + 11174042880 z^6 - 27562913280 z^7 + 19958641920 z^8 - 6647262720 z^9 + 1175427072 z^10 - 116238336 z^11 + 6393856 z^12 - 181248 z^13 + 2048 z^14) - (1/3274425) ((512 Sqrt[Pi] (38556000 z^(13/2) - 68886720 z^(15/2) + 44558640 z^(17/2) - 14031360 z^(19/2) + 2403450 z^(21/2) - 233100 z^(23/2) + 12663 z^(25/2) - 356 z^(27/2) + 4 z^(29/2)) Erfi[Sqrt[z]])/E^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]