Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.ai3o)

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=2, a₂>=2

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

For fixed z and a₁=2, a₂=9/2, b₁=-9/2

http://functions.wolfram.com/07.25.03.ai3o.01

Input Form

HypergeometricPFQ[{2, 9/2}, {-(9/2), -(7/2)}, -z] == (1/10418625) (10418625 - 5953500 z + 5613300 z^2 - 12972960 z^3 + 162162000 z^4 + 6616209600 z^5 - 59127606720 z^6 + 102801484800 z^7 - 69810902784 z^8 + 23234442240 z^9 - 4191267840 z^10 + 425926656 z^11 - 24129536 z^12 + 704512 z^13 - 8192 z^14) + (1/10418625) ((4096 Sqrt[Pi] (-4717440 z^(11/2) + 22498560 z^(13/2) - 31691520 z^(15/2) + 19474560 z^(17/2) - 6138720 z^(19/2) + 1072512 z^(21/2) - 106848 z^(23/2) + 5976 z^(25/2) - 173 z^(27/2) + 2 z^(29/2)) 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]