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Orthogonal Polynomials Associated with Complementary Chain Sequences
Kiran Kumar Beheraa, A. Sri Rangab, A. Swaminathana a Department of Mathematics, Indian Institute of Technology Roorkee,
Uttarakhand-247667, India
b Departamento de Matemática Aplicada, IBILCE, UNESP-Univ. Estadual Paulista, 15054-000, São José do Rio Preto, SP, Brazil
Abstract:
Using the minimal parameter sequence of a given chain sequence, we introduce the concept of complementary chain sequences, which we view as perturbations of chain sequences. Using the relation between these complementary chain sequences and the corresponding Verblunsky coefficients, the para-orthogonal polynomials and the associated Szegő polynomials are analyzed. Two illustrations, one involving Gaussian hypergeometric functions
and the other involving Carathéodory functions are also provided. A connection between these two illustrations by means of complementary chain sequences is also observed.
Keywords:
chain sequences; orthogonal polynomials; recurrence relation; Verblunsky coefficients; continued fractions; Carathéodory functions; hypergeometric functions.
Received: March 17, 2016; in final form July 22, 2016; Published online July 27, 2016
Citation:
Kiran Kumar Behera, A. Sri Ranga, A. Swaminathan, “Orthogonal Polynomials Associated with Complementary Chain Sequences”, SIGMA, 12 (2016), 075, 17 pp.
Linking options:
https://www.mathnet.ru/eng/sigma1157 https://www.mathnet.ru/eng/sigma/v12/p75
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Abstract page: | 181 | Full-text PDF : | 35 | References: | 32 |
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