Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.anz9)

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=6, a₂>=6

For fixed z and a₁=6, a₂=6, b₁>=-11/2

For fixed z and a₁=6, a₂=6, b₁=-5/2

http://functions.wolfram.com/07.25.03.anz9.01

Input Form

HypergeometricPFQ[{6, 6}, {-(5/2), 1}, z] == (1/13824000) (13824000 - 199065600 z + 1625702400 z^2 - 23121100800 z^3 - 126395751375 z^4 - 180151182450 z^5 - 113784394080 z^6 - 38154653280 z^7 - 7398275040 z^8 - 862708160 z^9 - 60871680 z^10 - 2522624 z^11 - 56064 z^12 - 512 z^13) + (1/27648000) (E^z Sqrt[Pi] (-107705394225 z^(7/2) - 372314943000 z^(9/2) - 448580164500 z^(11/2) - 260016768000 z^(13/2) - 82976061600 z^(15/2) - 15604197120 z^(17/2) - 1783900800 z^(19/2) - 124211200 z^(21/2) - 5100800 z^(23/2) - 112640 z^(25/2) - 1024 z^(27/2)) 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]