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Orthogonal Polynomials Associated with Complementary Chain Sequences
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- Фізико-технічні та математичні науки
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- Відділення математики
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2016, том 12
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Orthogonal Polynomials Associated with Complementary Chain Sequences
Інший ID:
2010 Mathematics Subject Classification: 42C05; 33C45; 30B70
DOI:10.3842/SIGMA.2016.075
DOI:10.3842/SIGMA.2016.075
Посилання:
Orthogonal Polynomials Associated with Complementary Chain Sequences / K.K. Behera, A. Sri Ranga, A. Swaminathan // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 27 назв. — англ.
Підтримка:
This paper is a contribution to the Special Issue on Orthogonal Polynomials, Special Functions and Applications.
The full collection is available at http://www.emis.de/journals/SIGMA/OPSFA2015.html.
nts
The authors wish to thank the anonymous referees for their constructive criticism that resulted
in significant improvement of the content leading to the final version. 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).
Дата:
2016
Переглядів:
485
Завантажень:
241
Анотація:
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.
