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Characterizations of classical orthogonal polynomials on quadratic lattices |
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| Authors: | Marlyse Njinkeu Sandjon Amílcar Branquinho Mama Foupouagnigni |
| Affiliation: | 1. Faculty of Sciences, Department of Mathematics, University of Yaounde I, Yaounde, Cameroon.;2. Faculty of Sciences and Technology, Department of Mathematics, University of Coimbra, Coimbra, Portugal.;3. Department of Mathematics of the Higher Teachers’ Training College, University of Yaounde I, Yaounde, Cameroon.;4. African Institute for Mathematical Sciences, AIMS-Cameroon, Limbe, Cameroon. |
| Abstract: | This paper is devoted to characterizations of classical orthogonal polynomials on quadratic lattices by using a matrix approach. In this form we recover the Hahn, Geronimus, Tricomi and Bochner type characterizations of classical orthogonal polynomials on quadratic lattices. Moreover a new matrix characterization of classical ortho-gonal polynomials in quadratic lattices is presented. From the Bochner type characterization we derive the three-term recurrence relation coefficients for these polynomials. |
| Keywords: | Classical orthogonal polynomials quadratic lattices characterization theorems divided-difference operators |