A Description of Second Degree Semiclassical Forms of Class Two Arising Via Cubic Decomposition

Khalfallah, Mohamed

doi:10.1007/s00009-021-01948-6

Cited by 4 publications

(2 citation statements)

References 23 publications

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“…Lemma 5 [13] Let ω 1 and ω 2 be two forms in P ′ and g(x) = N i=0 λ i x i ∈ P. The following statements are equivalent.…”

Section: Description Via Third Degree Character Of a Family Of Semicl...mentioning

confidence: 99%

“…A next natural step is to describe the third degree semiclassical forms of class two. 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%

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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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“…Lemma 5 [13] Let ω 1 and ω 2 be two forms in P ′ and g(x) = N i=0 λ i x i ∈ P. The following statements are equivalent.…”

Section: Description Via Third Degree Character Of a Family Of Semicl...mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Khalfallah

2022

Preprint

Self Cite

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Some characterizations of the symmetric q -Dunkl-semiclassical orthogonal q -polynomials

Srivastava,

Souissi,

Khalfallah

2023

Journal of Difference Equations and Applications

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On the characterizations of third-degree semiclassical forms via polynomial mappings

Marcellán

Khalfallah

2022

Integral Transforms and Special Functions

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A Description of Second Degree Semiclassical Forms of Class Two Arising Via Cubic Decomposition

Cited by 4 publications

References 23 publications

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

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

Some characterizations of the symmetric q -Dunkl-semiclassical orthogonal q -polynomials

On the characterizations of third-degree semiclassical forms via polynomial mappings

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