کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4607144 | 1631428 | 2014 | 30 صفحه PDF | دانلود رایگان |
Using Casorati determinants of Charlier polynomials (cna)n, we construct for each finite set FF of positive integers a sequence of polynomials cnF, n∈σFn∈σF, which are eigenfunctions of a second order difference operator, where σFσF is certain infinite set of nonnegative integers, σF⊊NσF⊊N. For suitable finite sets FF (we call them admissible sets), we prove that the polynomials cnF, n∈σFn∈σF, are actually exceptional Charlier 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 Charlier polynomials into a Wronskian determinant of Hermite polynomials. For admissible sets, these Wronskian determinants turn out to be exceptional Hermite polynomials.
Journal: Journal of Approximation Theory - Volume 182, June 2014, Pages 29–58