Abstract
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 K n ( λ, M, k) associated with the probability measure d φ( 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 K n ( λ, M) which are the symmetric Koornwinder polynomials. Monotonicity properties of the zeros of K n ( λ, M, k) in relation to M and k are also given.
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