Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.akb0)

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, a₂>=3

For fixed z and a₁=3, a₂=9/2, b₁>=-11/2

For fixed z and a₁=3, a₂=9/2, b₁=-11/2

http://functions.wolfram.com/07.25.03.akb0.01

Input Form

HypergeometricPFQ[{3, 9/2}, {-(11/2), -(11/2)}, -z] == (1/11345882625) (11345882625 - 5063451750 z + 2750517000 z^2 - 2432430000 z^3 + 4378374000 z^4 - 23156733600 z^5 + 1173274502400 z^6 - 48195987033600 z^7 + 198592332422400 z^8 - 275524843507200 z^9 + 179878555146240 z^10 - 64414076866560 z^11 + 13729169879040 z^12 - 1819246141440 z^13 + 152495063040 z^14 - 8031076352 z^15 + 255787008 z^16 - 4472832 z^17 + 32768 z^18) - (1/11345882625) ((8192 Sqrt[Pi] (925344000 z^(13/2) - 11967782400 z^(15/2) + 35349955200 z^(17/2) - 42057792000 z^(19/2) + 25260984000 z^(21/2) - 8609328000 z^(23/2) + 1778747040 z^(25/2) - 230929920 z^(27/2) + 19090350 z^(29/2) - 995700 z^(31/2) + 31495 z^(33/2) - 548 z^(35/2) + 4 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]