Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.a8ir)

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=-5/2, a₂>=-5/2

For fixed z and a₁=-5/2, a₂=6, b₁>=-11/2

For fixed z and a₁=-5/2, a₂=6, b₁=-9/2

http://functions.wolfram.com/07.25.03.a8ir.01

Input Form

HypergeometricPFQ[{-(5/2), 6}, {-(9/2), -(1/2)}, -z] == (1/15120) (15120 + 100800 z - 32130 z^2 - 72660 z^3 - 30807 z^4 + 34704 z^5 - 7600 z^6 + 608 z^7 - 16 z^8) + (1/30240) ((Sqrt[Pi] (-270270 z^(3/2) + 135135 z^(7/2) + 90090 z^(9/2) - 76440 z^(11/2) + 15792 z^(13/2) - 1232 z^(15/2) + 32 z^(17/2)) 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]