Chain sequences and symmetric generalized orthogonal polynomials

摘要

In this paper, we derive an explicit expression for the parameter sequences of a chain sequence in terms of the corresponding orthogonal polynomials and their associated polynomials. We use this to study the orthogonal polynomials Kn(λ,M,k) associated with the probability measure dφ(λ,M,k;x), which is the Gegenbauer measure of parameter λ+1 with two additional mass points at ±k. When k=1 we obtain information on the polynomials Kn(λ,M) which are the symmetric Koornwinder polynomials. Monotonicity properties of the zeros of Kn(λ,M,k) in relation to M and k are also given.