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Discrete Entropies of Chebyshev Polynomials

Author

Listed:
  • Răzvan-Cornel Sfetcu

    (Faculty of Mathematics and Computer Science, University of Bucharest, Str. Academiei 14, 010014 Bucharest, Romania)

  • Sorina-Cezarina Sfetcu

    (Faculty of Mathematics and Computer Science, University of Bucharest, Str. Academiei 14, 010014 Bucharest, Romania)

  • Vasile Preda

    (Faculty of Mathematics and Computer Science, University of Bucharest, Str. Academiei 14, 010014 Bucharest, Romania
    “Gheorghe Mihoc-Caius Iacob” Institute of Mathematical Statistics and Applied Mathematics, Calea 13 Septembrie 13, 050711 Bucharest, Romania
    “Costin C. Kiriţescu” National Institute of Economic Research, Calea 13 Septembrie 13, 050711 Bucharest, Romania)

Abstract

Because of its flexibility and multiple meanings, the concept of information entropy in its continuous or discrete form has proven to be very relevant in numerous scientific branches. For example, it is used as a measure of disorder in thermodynamics, as a measure of uncertainty in statistical mechanics as well as in classical and quantum information science, as a measure of diversity in ecological structures and as a criterion for the classification of races and species in population dynamics. Orthogonal polynomials are a useful tool in solving and interpreting differential equations. Lately, this subject has been intensively studied in many areas. For example, in statistics, by using orthogonal polynomials to fit the desired model to the data, we are able to eliminate collinearity and to seek the same information as simple polynomials. In this paper, we consider the Tsallis, Kaniadakis and Varma entropies of Chebyshev polynomials of the first kind and obtain asymptotic expansions. In the particular case of quadratic entropies, there are given concrete computations.

Suggested Citation

  • Răzvan-Cornel Sfetcu & Sorina-Cezarina Sfetcu & Vasile Preda, 2024. "Discrete Entropies of Chebyshev Polynomials," Mathematics, MDPI, vol. 12(7), pages 1-11, March.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:7:p:1046-:d:1367664
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    References listed on IDEAS

    as
    1. F. Clementi & M. Gallegati & G. Kaniadakis, 2009. "A k-generalized statistical mechanics approach to income analysis," Papers 0902.0075, arXiv.org, revised Feb 2009.
    2. Vikas Kumar & Rekha Rani, 2018. "Quantile Approach of Dynamic Generalized Entropy (Divergence) Measure," Statistica, Department of Statistics, University of Bologna, vol. 78(2), pages 105-126.
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