Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.ajg1)

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=5/2, a₂>=5/2

For fixed z and a₁=5/2, a₂=5, b₁>=-11/2

For fixed z and a₁=5/2, a₂=5, b₁=-11/2

http://functions.wolfram.com/07.25.03.ajg1.01

Input Form

HypergeometricPFQ[{5/2, 5}, {-(11/2), -(3/2)}, z] == (1/280665) (280665 + 425250 z + 1984500 z^2 - 11907000 z^3 + 34927200 z^4 - 108972864 z^5 + 778377600 z^6 + 1885939200 z^7 + 1344754944 z^8 + 441568512 z^9 + 77048832 z^10 + 7523568 z^11 + 408864 z^12 + 11456 z^13 + 128 z^14) + (1/280665) (8 E^z Sqrt[Pi] (170931600 z^(13/2) + 300839616 z^(15/2) + 191845584 z^(17/2) + 59599008 z^(19/2) + 10077489 z^(21/2) + 965304 z^(23/2) + 51816 z^(25/2) + 1440 z^(27/2) + 16 z^(29/2)) 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]