Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.ab7e)

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=-1/2, a₂>=-1/2

For fixed z and a₁=-1/2, a₂=2, b₁>=-11/2

For fixed z and a₁=-1/2, a₂=2, b₁=-11/2

http://functions.wolfram.com/07.25.03.ab7e.01

Input Form

HypergeometricPFQ[{-(1/2), 2}, {-(11/2), -(7/2)}, -z] == (1/1091475) (1091475 + 56700 z - 3780 z^2 + 1440 z^3 - 3600 z^4 - 20160 z^5 - 141120 z^6 + 248832 z^7 - 97536 z^8 + 12800 z^9 - 512 z^10) + (256 Sqrt[Pi] (900 z^(13/2) - 1140 z^(15/2) + 405 z^(17/2) - 51 z^(19/2) + 2 z^(21/2)) Erfi[Sqrt[z]])/(E^z 1091475)

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]