Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.ab7r)

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.ab7r.01

Input Form

HypergeometricPFQ[{-(1/2), 2}, {-(11/2), 5/2}, z] == (20160 - 9015 z + 2748 z^2 - 588 z^3 + 88 z^4 - 8 z^5)/(3465 z) - (4 E^z Sqrt[Pi] (2520 - 3240 z + 1800 z^2 - 600 z^3 + 135 z^4 - 21 z^5 + 2 z^6) Erf[Sqrt[z]])/(3465 z^(3/2))

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]