Download PDF - Recurrence relations with periodic coefficients and Chebyshev polynomialsAll rights reserved. Copyright exceptions and limitations apply

ArticleOriginal scientific text

Title

Recurrence relations with periodic coefficients and Chebyshev polynomials

Authors 1, 2, 2

Affiliations

  1. Laboratoire d'Analyse Numérique, et d'Optimisation, UFR IEEA-M3, USTL Flandres-Artois
  2. Phymat, Université de Toulon et du Var, B.P. 132, 83957 la Garde Cedex, France, 59655 Villeneuve d'Ascq Cedex, France

Abstract

We show that polynomials defined by recurrence relations with periodic coefficients may be represented with the help of Chebyshev polynomials of the second kind.

Keywords

ENG
orthogonal polynomials, periodic coefficients of recurrence relation

Bibliography

  1. T. S. Chihara, An Introduction to Orthogonal Polynomials, Gordon and Breach, 1978.
  2. J. S. Geronimo and W. Van Assche, Orthogonal polynomials with asymptotically periodic recurrence coefficients, J. Approx. Theory 46 (1986), 251-283.
  3. J. S. Geronimo and W. Van Assche, Approximating the weight function for orthogonal polynomials on several intervals, ibid. 65 (1991), 341-371.
  4. H. S. Wall, Analytic Theory of Continued Fractions, D. Van Nostrand, 1967.
Applicationes Mathematicae
1995-1996/23/3
Export to PBN, Opens in new tab
Pages:
319-323
Main language of publication
English
Received
1994-09-26
Published
1995
Exact and natural sciences