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

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=-5/2

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

Input Form

HypergeometricPFQ[{3/2, 6}, {-(5/2), -(3/2)}, -z] == (1/1350) (1350 - 3240 z + 37800 z^2 + 1411200 z^3 - 11174760 z^4 + 16938900 z^5 - 9815988 z^6 + 2708505 z^7 - 388620 z^8 + 29432 z^9 - 1104 z^10 + 16 z^11) + (1/2700) ((Sqrt[Pi] (-7876440 z^(7/2) + 33693660 z^(9/2) - 41729220 z^(11/2) + 22015935 z^(13/2) - 5778810 z^(15/2) + 805608 z^(17/2) - 59952 z^(19/2) + 2224 z^(21/2) - 32 z^(23/2)) 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]