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

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=3, b₁>=-11/2

For fixed z and a₁=1/2, a₂=3, b₁=-11/2

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

Input Form

HypergeometricPFQ[{1/2, 3}, {-(11/2), 5/2}, -z] == (-20160 - 11895 z - 4518 z^2 - 1272 z^3 - 280 z^4 - 48 z^5 - 4 z^6 + 8 z^7)/ (3465 z) - (1/(3465 z^(3/2))) ((2 Sqrt[Pi] (-5040 - 7200 z - 4680 z^2 - 1920 z^3 - 570 z^4 - 132 z^5 - 25 z^6 - 4 z^7 + 4 z^8) 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]