Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.al2r)

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=-9/2

http://functions.wolfram.com/07.25.03.al2r.01

Input Form

HypergeometricPFQ[{7/2, 4}, {-(9/2), -(3/2)}, -z] == (1/127575) (127575 - 264600 z + 1701000 z^2 + 14968800 z^3 + 75675600 z^4 + 726485760 z^5 - 2441537280 z^6 + 2215603200 z^7 - 886959360 z^8 + 183459840 z^9 - 20810752 z^10 + 1293696 z^11 - 40960 z^12 + 512 z^13) - (1/127575) ((64 Sqrt[Pi] (22276800 z^(11/2) - 50979600 z^(13/2) + 40440960 z^(15/2) - 15151920 z^(17/2) + 3019800 z^(19/2) - 334965 z^(21/2) + 20530 z^(23/2) - 644 z^(25/2) + 8 z^(27/2)) 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]