Exceptional Meixner and Laguerre orthogonal polynomials
Using Casorati determinants of Meixner polynomials (manc)n, we construct for each pair F 0 (F1, F2) of finite sets of positive integers a sequence of polynomials manc;F, n E r F, which are eigenfunctions of a second order difference operator, where rF is certain infinite set of nonnegative integers,...
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| Format: | Article |
| Status: | Published version |
| Publication date: | 2014 |
| Country: | España |
| Institution: | Universidad de Sevilla (US) |
| Repository: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/182368 |
| Online Access: | https://hdl.handle.net/11441/182368 https://doi.org/10.1016/j.jat.2014.05.009 |
| Access Level: | Open access |
| Keyword: | Orthogonal polynomials Exceptional orthogonal polynomial Difference operators Differential operators Meixner polynomials Krawtchouk polynomials Laguerre polynomials |
| Summary: | Using Casorati determinants of Meixner polynomials (manc)n, we construct for each pair F 0 (F1, F2) of finite sets of positive integers a sequence of polynomials manc;F, n E r F, which are eigenfunctions of a second order difference operator, where rF is certain infinite set of nonnegative integers, rF C N. When c and F satisfy a suitable admissibility condition, we prove that the polynomials manc;F, n E rF , are actually exceptional Meixner polynomials; that is, in addition, they are orthogonal and complete with respect to a positive measure. By passing to the limit, we transform the Casorati determinant of Meixner polynomials into a Wronskian type determinant of Laguerre polynomials (Lan)n. Under the admissibility conditions for F and r, these Wronskian type determinants turn out to be exceptional Laguerre polynomials. |
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