Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.1718)

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=-11/2, a₂>=-11/2

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

For fixed z and a₁=-11/2, a₂=3, b₁=1

http://functions.wolfram.com/07.25.03.1718.01

Input Form

HypergeometricPFQ[{-(11/2), 3}, {1, 7/2}, -z] == (1/(22020096 z^2)) ((-93555 - 228690 z + 18391548 z^2 + 53594760 z^3 + 35284848 z^4 + 8397728 z^5 + 792896 z^6 + 24960 z^7)/E^z) + (1/(44040192 z^(5/2))) (Sqrt[Pi] (93555 + 166320 z + 3492720 z^2 + 69854400 z^3 + 135828000 z^4 + 78236928 z^5 + 17563392 z^6 + 1610752 z^7 + 49920 z^8) Erf[Sqrt[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]