q-Classical Orthogonal Polynomials: A General Difference Calculus Approach
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- Costas-Santos, R.S. & Marcellán, F. Acta Appl Math (2010) 111: 107. doi:10.1007/s10440-009-9536-z
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It is well known that the classical families of orthogonal polynomials are characterized as the polynomial eigenfunctions of a second order homogeneous linear differential/difference hypergeometric operator with polynomial coefficients.
In this paper we present a study of the classical orthogonal polynomials sequences, in short classical OPS, in a more general framework by using the differential (or difference) calculus and Operator Theory. The Hahn’s Theorem and a characterization theorem for the q-polynomials which belongs to the q-Askey and Hahn tableaux are proved. Finally, we illustrate our results applying them to some known families of orthogonal q-polynomials.