Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.1906)

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=7/2, b₁>=-11/2

For fixed z and a₁=-11/2, a₂=7/2, b₁=-3/2

http://functions.wolfram.com/07.25.03.1906.01

Input Form

HypergeometricPFQ[{-(11/2), 7/2}, {-(3/2), 9/2}, -z] == (1/(165888 z^3)) ((-155925 - 103950 z - 41580 z^2 + 154008 z^3 - 309840 z^4 + 1351200 z^5 + 1246272 z^6 + 258944 z^7 + 14336 z^8)/E^z) + (Sqrt[Pi] (155925 + 3725568 z^6 + 2737152 z^7 + 532224 z^8 + 28672 z^9) Erf[Sqrt[z]])/(331776 z^(7/2))

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]