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Research Article

Study of an example of Markov chains involving Chebyshev polynomials

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Pages 180-195 | Received 22 Jan 2022, Accepted 01 Jul 2022, Published online: 18 Jul 2022

References

  • Alberto Grunbaum F. Random walks and orthogonal polynomials: some challenges. In: Pinsky M, Birnir B, editor. Probability, geometry and integrable systems. Vol. 55. MSRI Publications; 2007. p. 241–260.
  • Dilcher K, Stolarsky K. Resultants and discriminants of Chebyshev and related polynomials. Trans Amer Math Soc. 2004;357:965–981.
  • Gishe JE. A finite family of q-orthogonal polynomials and resultants of Chebyshev polynomials [graduate school theses and dissertations]. University of South Florida.
  • Eslahchia MR, Dehghanb M, Amani S. The third and fourth kinds of Chebyshev polynomials and best uniform approximation. Math Comput Model. 2012;55:1746–1762.
  • Milovanović GV, Cvestković AS, Mateji MM. Remark on orthogonal polynomials induced by the modified Chebychev measure of the second kind. Facta Universitatis (Nis) Ser Math Inform. 2006;21:13–21.
  • Shen J, Tang T, Wang L. Spectral methods: algorithms, analysis and applications. Springer Science & Business Media; 2011. (Springer series in computational mathematics; vol. 41).
  • Foupouagnigni M. On difference and differential equations for modifications of classical orthogonal polynomials [Habilitation thesis]. Kassel: Department of Mathematics and Computer Science, University of Kassel; 2006 Jan.
  • Abramowitz M, Stegun IA, editors. Handbook of mathematical functions. 10th ed. New York: Dover; 1972.
  • Masjed-Jamei M, Dehghan M. On rational classical orthogonal polynomials and their applications for explicit computation of inverse Laplace transforms. Math Probl Eng. 2005;2005(2):215–230.
  • Smirnov VJ, Lebedev NA. The constructive theory of functions of a complex variable. Moscow: Nauka; 1964 [in Russian]; Cambridge (MA): M.I.T. Press; 1968 [Engl. transl.].
  • Smirnov VI. Sur les formules de Cauchy et de Green et quelques proble? mes qui s'y rattachent, Bulletin de l'Académie des Sciences de l'URSS. Classe des sciences mathématiques et na. 1932;(3):337–372.
  • Marcellan F, Petrolinho J. Orthogonal polynomials and quadratic transformations. Port Math. 1999;56:Fasc.1.

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