A description via third degree character of quasi-symmetric semiclassical forms of class two

Khalfallah, Mohamed

doi:10.1007/s10998-022-00458-6

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2022

2024

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Cited by 4 publications

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“…This result was done only for the second degree semiclassical character and in the particular cases [7,13]. We should point out that, no examples of strict third degree semiclassical forms of class two have been analysed in the literature up to the recent contribution [14], for the particular case of quasi-symmetric forms.…”

Section: Introductionmentioning

confidence: 99%

Several characterizations of third degree semiclassical linear forms of class two appearing via cubic decomposition

Khalfallah

2022

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In this work we consider orthogonal polynomials via cubic decomposition in the framework of the third degree semiclassical class. Based on their third degree character, we give a complete description, by using the formal Stieltjes function and the moments, of semiclassical linear forms of class two arising from the cubic decomposition W3n(x) = Pn(x3); n ≥ 0. We focus our attention on the link between these forms and the strict third degree classical forms Vqk,l= J (k + q/3; l -q/3), q ∈{1,2},k,l ∈Z with k+ l≥ -1. All of them are rational transformations of the Jacobi form V = J (-2/3;-1=3).

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Section: Introductionmentioning

confidence: 99%