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

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=4, b₁>=-11/2

For fixed z and a₁=-1/2, a₂=4, b₁=-11/2

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

Input Form

HypergeometricPFQ[{-(1/2), 4}, {-(11/2), 11/2}, -z] == (3175200 + 831600 z + 231840 z^2 + 48300 z^3 + 7686 z^4 + 927 z^5 + 80 z^6 + 4 z^7)/(264 z^4) + (1/(528 z^(9/2))) ((Sqrt[Pi] (-3175200 - 2948400 z - 1350720 z^2 - 404460 z^3 - 87750 z^4 - 14355 z^5 - 1770 z^6 - 156 z^7 - 8 z^8) Erfi[Sqrt[z]])/E^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]