Publication
A characterization theorem for semi-classical orthogonal polynomials on non-uniform lattices
| Summary: | It is proved a characterization theorem for semi-classical orthogonal polynomials on non- uniform lattices that states the equivalence between the Pearson equation for the weight and some systems involving the orthogonal polynomials as well as the functions of the second kind. As a consequence, it is deduced the analogue of the so-called compatibility conditions in the ladder operator scheme. The classical orthogonal polynomials on non- uniform lattices are then recovered under such compatibility conditions, through a closed formula for the recurrence relation coefficients. |
|---|---|
| Main Authors: | Rebocho, M. N. |
| Other Authors: | Filipuk, Galina; Chen, Yang; Branquinho, A. |
| Subject: | Orthogonal polynomials Divided-difference operator Non-uniform lattices Askey-Wilson operator Semi-classical class |
| Year: | 2018 |
| Country: | Portugal |
| Document type: | preprint |
| Access type: | open access |
| Associated institution: | Universidade da Beira Interior |
| Language: | English |
| Origin: | uBibliorum |
| Summary: | It is proved a characterization theorem for semi-classical orthogonal polynomials on non- uniform lattices that states the equivalence between the Pearson equation for the weight and some systems involving the orthogonal polynomials as well as the functions of the second kind. As a consequence, it is deduced the analogue of the so-called compatibility conditions in the ladder operator scheme. The classical orthogonal polynomials on non- uniform lattices are then recovered under such compatibility conditions, through a closed formula for the recurrence relation coefficients. |
|---|