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

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=3/2, a₂>=3/2

For fixed z and a₁=3/2, a₂=6, b₁>=-11/2

For fixed z and a₁=3/2, a₂=6, b₁=-11/2

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

Input Form

HypergeometricPFQ[{3/2, 6}, {-(11/2), -(11/2)}, -z] == (1/1620840375) (1620840375 - 482233500 z + 208372500 z^2 - 158760000 z^3 + 257191200 z^4 - 1257379200 z^5 + 59935075200 z^6 - 2327541350400 z^7 + 9109518163200 z^8 - 12054584424960 z^9 + 7529716938240 z^10 - 2586035168640 z^11 + 529663236480 z^12 - 67555494720 z^13 + 5458255296 z^14 - 277424128 z^15 + 8537088 z^16 - 144384 z^17 + 1024 z^18) - (1/1620840375) ((32 Sqrt[Pi] (11794280400 z^(13/2) - 145462791600 z^(15/2) + 410602840200 z^(17/2) - 467736330600 z^(19/2) + 269445389850 z^(21/2) - 88212487230 z^(23/2) + 17531943975 z^(25/2) - 2192373015 z^(27/2) + 174777330 z^(29/2) - 8800680 z^(31/2) + 269024 z^(33/2) - 4528 z^(35/2) + 32 z^(37/2)) 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]