Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.9990)

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=-5/2, a₂>=-5/2

For fixed z and a₁=-5/2, a₂=3, b₁>=-11/2

For fixed z and a₁=-5/2, a₂=3, b₁=7/2

http://functions.wolfram.com/07.25.03.9990.01

Input Form

HypergeometricPFQ[{-(5/2), 3}, {7/2, 6}, z] == (20 (12 + 30 z + 65 z^2))/(1001 z^5) + (1/(96096 z^5)) (E^z (-23040 - 34560 z - 78720 z^2 - 35295 z^3 - 28020 z^4 + 35752 z^5 - 6832 z^6 + 336 z^7)) + (Sqrt[Pi] (135135 + 64350 z + 85800 z^2 - 78000 z^3 + 14000 z^4 - 672 z^5) Erfi[Sqrt[z]])/(192192 z^(5/2))

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]