Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.a99n)

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=-3/2, a₂>=-3/2

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

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

http://functions.wolfram.com/07.25.03.a99n.01

Input Form

HypergeometricPFQ[{-(3/2), 2}, {-(11/2), -(7/2)}, -z] == (1/363825) (363825 + 56700 z + 3780 z^2 - 480 z^3 + 720 z^4 + 2880 z^5 + 15680 z^6 - 18432 z^7 + 4352 z^8 - 256 z^9) + (128 Sqrt[Pi] (-180 z^(13/2) + 160 z^(15/2) - 35 z^(17/2) + 2 z^(19/2)) Erfi[Sqrt[z]])/(E^z 363825)

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]