Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.9989)

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=3, b₁>=-11/2

For fixed z and a₁=-5/2, a₂=3, b₁=7/2

http://functions.wolfram.com/07.25.03.9989.01

Input Form

HypergeometricPFQ[{-(5/2), 3}, {7/2, 5}, -z] == -((40 (-3 + 13 z))/(1001 z^4)) + (-23040 + 76800 z - 46815 z^2 + 46080 z^3 + 77456 z^4 + 17696 z^5 + 1008 z^6)/(E^z (192192 z^4)) + (Sqrt[Pi] (135135 - 90090 z + 154440 z^2 + 171600 z^3 + 36400 z^4 + 2016 z^5) Erf[Sqrt[z]])/(384384 z^(5/2))

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]