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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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| Authors: | Stanisław Lewanowicz Eduardo Godoy Iván Area André Ronveaux Alejandro Zarzo |
| Affiliation: | (1) Institute of Computer Science, University of Wrocław, ul, Przesmyckiego 20, 51-151 Wrocław, Poland;(2) Departamento de Matemática Aplicada, E.T.S.I. Industriales y Minas, Universidad de Vigo, Campus Lagoas-Marcosende, E-36200 Vigo, Spain;(3) Physique Mathematique, Facultés Universitaires N. D. de la Paix, 61 Rue de Bruxelles, B-5000 Namur, Belgium;(4) Departamento de Matemática Aplicada, E.T.S.I. Industriales, Universidad Politécnica de Madrid, E-28006 Madrid, Spain |
| 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. This revised version was published online in June 2006 with corrections to the Cover Date. |
| Keywords: | recurrence relations q-difference equations q-classical orthogonal polynomials q-Hahn class Fourier coefficients linearization problem connection problem 33C25 33D45 |
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