Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4607164 | Journal of Approximation Theory | 2014 | 33 Pages |
Abstract
Using Casorati determinants of Meixner polynomials (mna,c)n, we construct for each pair F=(F1,F2) of finite sets of positive integers a sequence of polynomials mna,c;F, nâÏF, which are eigenfunctions of a second order difference operator, where ÏF is certain infinite set of nonnegative integers, ÏFâï¸N. When c and F satisfy a suitable admissibility condition, we prove that the polynomials mna,c;F, nâÏF, 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 (Lnα)n. Under the admissibility conditions for F and α, these Wronskian type determinants turn out to be exceptional Laguerre polynomials.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Antonio J. Durán,