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

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=-9/2

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

Input Form

HypergeometricPFQ[{3, 9/2}, {-(9/2), -(5/2)}, -z] == (1/1488375) (1488375 - 1786050 z + 3742200 z^2 - 32432400 z^3 - 486486000 z^4 - 7718911200 z^5 + 41988360960 z^6 - 55284042240 z^7 + 30968421120 z^8 - 8907717120 z^9 + 1430046720 z^10 - 131960832 z^11 + 6888448 z^12 - 187392 z^13 + 2048 z^14) - (1/1488375) ((512 Sqrt[Pi] (-35380800 z^(11/2) + 118843200 z^(13/2) - 132073200 z^(15/2) + 68055120 z^(17/2) - 18680760 z^(19/2) + 2915640 z^(21/2) - 264285 z^(23/2) + 13635 z^(25/2) - 368 z^(27/2) + 4 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]