New examples of Krall-Meixner and Krall-Hahn polynomials, with applications to the construction of exceptional Meixner and Laguerre polynomials

Abstract

We construct new examples of Krall discrete orthogonal polynomials, i.e., orthogonal polynomials with respect to a measure which are also eigenfunctions of a higher order difference operator. The new examples include the orthogonal polynomials with respect to the measures obtained from the Meixner measure ρa,c and Hahn measure ρ a,b,N by removing a finite number of their mass points when the parameter c of the Meixner measure and a or b of the Hahn measure are positive integers. From the new Krall-Meixner families we construct new families of exceptional Meixner and Laguerre polynomials. * Partially supported by PGC2018-096504-B-C31 (FEDER(EU)/Ministerio de Ciencia e Innovación-Agencia Estatal de Investigación), FQM-262 and Feder-US-1254600 (FEDER(EU)/Junta de Andalucía).