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

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=4, b₁>=-11/2

For fixed z and a₁=3/2, a₂=4, b₁=-11/2

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

Input Form

HypergeometricPFQ[{3/2, 4}, {-(11/2), 1/2}, -z] == (1/31185) (31185 + 68040 z + 63000 z^2 + 50400 z^3 + 45360 z^4 + 59136 z^5 + 209664 z^6 - 148560 z^7 + 30736 z^8 - 2432 z^9 + 64 z^10) - (8 Sqrt[Pi] (33915 z^(13/2) - 20349 z^(15/2) + 3990 z^(17/2) - 308 z^(19/2) + 8 z^(21/2)) Erfi[Sqrt[z]])/(E^z 31185)

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]