Interlacing of zeros of quasi-orthogonal meixner polynomials

Abstract

We consider the interlacing of zeros of polynomials within the sequences of quasi-orthogonal order one Meixner polynomials {M_n(x;β; c)∞ n=1 characterised by β; c ∈ (0; 1). The interlacing of zeros of quasi-orthogonal Meixner polynomials M_n(x;β; c) with the zeros of their nearest orthogonal counterparts Mt(x;β + k; c), l; n ∈ ℕ, k ∈ {1; 2}; is also discussed.

Mathematics Subject Classication (2010): 33C45, 42C05.

Key words: Discrete orthogonal polynomials, quasi-orthogonal polynomials, Meixner
polynomials, interlacing of zeros.