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

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=2, a₂>=2

For fixed z and a₁=2, a₂=5, b₁>=-11/2

For fixed z and a₁=2, a₂=5, b₁=-5/2

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

Input Form

HypergeometricPFQ[{2, 5}, {-(5/2), 1}, z] == (1/720) (720 - 2880 z + 8640 z^2 - 53760 z^3 - 95055 z^4 - 43872 z^5 - 7984 z^6 - 608 z^7 - 16 z^8) + (1/1440) (E^z Sqrt[Pi] (-173745 z^(7/2) - 227370 z^(9/2) - 95160 z^(11/2) - 16560 z^(13/2) - 1232 z^(15/2) - 32 z^(17/2)) 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]