Chain sequences and symmetric generalized orthogonal polynomials

Authors:
C. F. Bracciali;D. K. Dimitrov;A. Sri Ranga
Affiliations:
Departamento de Ciências de Computação e Estatística, Instituto de Biociências, Letras e Ciências Exatas, Universidade Estadual Paulista (UNESP), SP, Brazil;Departamento de Ciências de Computação e Estatística, Instituto de Biociências, Letras e Ciências Exatas, Universidade Estadual Paulista (UNESP), SP, Brazil;Departamento de Ciências de Computação e Estatística, Instituto de Biociências, Letras e Ciências Exatas, Universidade Estadual Paulista (UNESP), SP, Brazil
Venue:
Journal of Computational and Applied Mathematics
Year:
2002

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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 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.