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

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=4, a₂>=4

For fixed z and a₁=4, a₂=9/2, b₁>=-11/2

For fixed z and a₁=4, a₂=9/2, b₁=-9/2

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

Input Form

HypergeometricPFQ[{4, 9/2}, {-(9/2), -(9/2)}, -z] == (1/281302875) (281302875 - 250047000 z + 280665000 z^2 - 583783200 z^3 + 3405402000 z^4 - 185253868800 z^5 + 8095834656000 z^6 - 35210696371200 z^7 + 51232139400960 z^8 - 34911979776000 z^9 + 13001957406720 z^10 - 2873697361920 z^11 + 393924464640 z^12 - 34089271296 z^13 + 1850173440 z^14 - 60635136 z^15 + 1089536 z^16 - 8192 z^17) + (1/281302875) ((1024 Sqrt[Pi] (1202947200 z^(11/2) - 16378588800 z^(13/2) + 50708851200 z^(15/2) - 63006854400 z^(17/2) + 39399242400 z^(19/2) - 13942484640 z^(21/2) + 2984052960 z^(23/2) - 400502880 z^(25/2) + 34165395 z^(27/2) - 1835895 z^(29/2) + 59742 z^(31/2) - 1068 z^(33/2) + 8 z^(35/2)) 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]