Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.ake4)

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=-3/2

http://functions.wolfram.com/07.25.03.ake4.01

Input Form

HypergeometricPFQ[{3, 9/2}, {-(3/2), 1/2}, -z] == (1/315) (315 + 5670 z + 83160 z^2 - 357840 z^3 + 334800 z^4 - 118944 z^5 + 18688 z^6 - 1296 z^7 + 32 z^8) - ((8/315) Sqrt[Pi] (22680 z^(5/2) - 60480 z^(7/2) + 48300 z^(9/2) - 15960 z^(11/2) + 2415 z^(13/2) - 164 z^(15/2) + 4 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]