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A positive definite linear functional of class \(s=2\), generalization of Chebyshev polynomials

  • Mohamed Ihssen Tounsi
  • Majed Benabdallah
  • Mohamed Jalel AtiaEmail author
Article
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Abstract

In the present work we deal with the quadratic decomposition of symmetric semiclassical polynomial sequences of class 2 orthogonal with respect to the positive definite weight \( | x^2-\frac{1}{2} |^p(1-x^2)^{-\frac{1}{2}}\), \( p > -1\), on \([-1,1]\). The coefficients of the three-term recurrence relation, the structure relation, the differential equation as well as some information about the zeros of the corresponding orthogonal polynomials are given. These results reduce to the Chebyshev case for \(p=0\).

Keywords

Orthogonal polynomials Symmetric sequences Semiclassical sequences Quadratic decomposition 

Mathematics Subject Classification

33C45 42C05 

Notes

Acknowledgements

We would sincerely like to express special thanks to the referees for their interest and careful reading. Moreover, we are particularly indebted to them for suggesting to add either Proposition 4.2 and its corollary or the last section.

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Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2019

Authors and Affiliations

  1. 1.Gabes UniversityGabèsTunisia
  2. 2.Qassim UniversityBuraydahKingdom of Saudi Arabia

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