Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.1404)

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=2, b₁>=-11/2

For fixed z and a₁=-11/2, a₂=2, b₁=4

http://functions.wolfram.com/07.25.03.1404.01

Input Form

HypergeometricPFQ[{-(11/2), 2}, {4, 5}, z] == (96 (-8 + 17 z))/(1105 z^3) + (1/(241158542625 z^3)) (128 E^(z/2) (1309458150 - 3411483075 z + 1024619040 z^2 + 2134694520 z^3 - 1749215520 z^4 + 532102320 z^5 - 79296000 z^6 + 6099264 z^7 - 229888 z^8 + 3328 z^9) BesselI[0, z/2]) - (1/(241158542625 z^3)) (128 E^(z/2) (103378275 - 1794085515 z + 1646893080 z^2 + 987964200 z^3 - 1319479920 z^4 + 461291760 z^5 - 73531584 z^6 + 5874368 z^7 - 226560 z^8 + 3328 z^9) BesselI[1, z/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]