Duran, Antonio J. , RUEDA GARCIA, MONICA
No
J. Approx. Theory
Article
Científica
0.993
0.689
01/03/2021
000607842600002
Meixner type polynomials (q(n))(n >= 0) are defined from the Meixner polynomials by using Casoratian determinants whose entries belong to two given finite sets of polynomials (S-h)(h=1)(m1)and (T-g)(g=1)(m2). They = are eigenfunctions of higher order difference operators but only for a careful choice of the polynomials (S-h)(h=1)(m1) and (T-g )(g=1)(m2), the sequence (q(n))(n >= 0) is orthogonal with respect to a measure. In this paper, we prove that the Meixner type polynomials (q(n))(n >= 0) always satisfy higher order recurrence relations (hence, they are bispectral). We also introduce and characterize the algebra of difference operators associated to these recurrence relations. Our characterization is constructive and surprisingly simple. As a consequence, we determine the unique choice of the polynomials (S-h)(h=1)(m1) and (T-g)(g=1)(m2) such that the sequence (q(n))(n >= 0) is orthogonal with respect to a measure. (C) 2020 Published by Elsevier Inc.
Orthogonal polynomials; Bispectral orthogonal polynomials; Recurrence relations; Algebra of difference operators; Meixner polynomials