Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.am1v)

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=4, a₂>=4

For fixed z and a₁=4, a₂=9/2, b₁>=-11/2

For fixed z and a₁=4, a₂=9/2, b₁=-3/2

http://functions.wolfram.com/07.25.03.am1v.01

Input Form

HypergeometricPFQ[{4, 9/2}, {-(3/2), -(1/2)}, -z] == (1/945) (945 - 22680 z - 1247400 z^2 + 13638240 z^3 - 26444880 z^4 + 18805248 z^5 - 6197952 z^6 + 1042080 z^7 - 91152 z^8 + 3904 z^9 - 64 z^10) + ((8/945) Sqrt[Pi] (498960 z^(5/2) - 2744280 z^(7/2) + 4213440 z^(9/2) - 2685060 z^(11/2) + 834750 z^(13/2) - 135723 z^(15/2) + 11634 z^(17/2) - 492 z^(19/2) + 8 z^(21/2)) 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]