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Recurrence relations for the coefficients of the Fourier series expansions with respect to q-classical orthogonal polynomials

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Abstract

We propose an algorithm to construct recurrence relations for the coefficients of the Fourier series expansions with respect to the q-classical orthogonal polynomials pk(x;q). Examples dealing with inversion problems, connection between any two sequences of q-classical polynomials, linearization of ϑm(x) pn(x;q), where ϑm(x) is xmor (x;q)m, and the expansion of the Hahn-Exton q-Bessel function in the little q-Jacobi polynomials are discussed in detail.

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Authors and Affiliations

  1. Institute of Computer Science, University of Wrocław, ul, Przesmyckiego 20, 51-151, Wrocław, Poland

    Stanisław Lewanowicz

  2. Departamento de Matemática Aplicada, E.T.S.I. Industriales y Minas, Universidad de Vigo, Campus Lagoas-Marcosende, E-36200, Vigo, Spain

    Eduardo Godoy & Iván Area

  3. Physique Mathematique, Facultés Universitaires N. D. de la Paix, 61 Rue de Bruxelles, B-5000, Namur, Belgium

    André Ronveaux

  4. Departamento de Matemática Aplicada, E.T.S.I. Industriales, Universidad Politécnica de Madrid, E-28006, Madrid, Spain

    Alejandro Zarzo

Authors
  1. Stanisław Lewanowicz
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  2. Eduardo Godoy
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  3. Iván Area
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  4. André Ronveaux
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  5. Alejandro Zarzo
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Lewanowicz, S., Godoy, E., Area, I. et al. Recurrence relations for the coefficients of the Fourier series expansions with respect to q-classical orthogonal polynomials. Numerical Algorithms 23, 31–50 (2000). https://doi.org/10.1023/A:1019139731216

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  • DOI: https://doi.org/10.1023/A:1019139731216