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Symmetry, Integrability and Geometry: Methods and Applications, 2016, Volume 12, 075, 17 pp.
DOI: https://doi.org/10.3842/SIGMA.2016.075 (Mi sigma1157) 		 
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
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DOI: https://doi.org/10.3842/SIGMA.2016.075
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.
Funding agency Grant number
National Council for Scientific and Technological Development (CNPq) 475502/2013-2
305073/2014-1
Fundação de Amparo à Pesquisa do Estado de São Paulo 2009/13832-9
The work of the second author was supported by funds from CNPq, Brazil (grants 475502/2013-2 and 305073/2014-1) and FAPESP, Brazil (grant 2009/13832-9).
Received: March 17, 2016; in final form July 22, 2016; Published online July 27, 2016
Bibliographic databases:
Document Type: Article
MSC: 42C05; 33C45; 30B70
Language: English
Citation: Kiran Kumar Behera, A. Sri Ranga, A. Swaminathan, “Orthogonal Polynomials Associated with Complementary Chain Sequences”, SIGMA, 12 (2016), 075, 17 pp.
Citation in format AMSBIB
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