Given a sequence of polynomials (pn)n, an algebra of operators A acting in the linear space of polynomials and an operator Dp∈A with Dp(pn)=θnpn, where θn is any arbitrary eigenvalue,
we construct a new sequence of polynomials (qn)n by considering a linear
combination of m+1 consecutive pn:
qn=pn+∑j=1mβn,jpn−j. Using the concept of
D-operator, we determine the structure of the sequences
βn,j,j=1,…,m, in order that the polynomials (qn)n are
eigenfunctions of an operator in the algebra A. As an application,
from the classical discrete family of Hahn polynomials we construct orthogonal
polynomials (qn)n which are also eigenfunctions of higher-order difference
operators.Comment: 26 pages. arXiv admin note: text overlap with arXiv:1307.1326,
arXiv:1407.697