Exceptional Hahn and Jacobi polynomials with an arbitrary number of continuous parameters
Abstract
We construct new examples of exceptional Hahn and Jacobi polynomials. Exceptional polynomials are orthogonal polynomials with respect to a measure which are also eigenfunctions of a second order difference or differential operator. The most apparent difference between classical or classical discrete orthogonal polynomials and their exceptional counterparts is that the exceptional families have gaps in their degrees, in the sense that not all degrees are present in the sequence of polynomials. The new examples have the novelty that they depend on an arbitrary number of continuous parameters.
 Publication:

arXiv eprints
 Pub Date:
 April 2021
 arXiv:
 arXiv:2104.01354
 Bibcode:
 2021arXiv210401354D
 Keywords:

 Mathematics  Classical Analysis and ODEs;
 42C05;
 33C45;
 33E30