Continued Fractions and Orthogonal Polynomials on the Unit Circle
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Date
2005
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Elsevier Science Bv
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HYBRID
Green Open Access
No
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Abstract
This survey is written to stress the role of continued fractions in the theory of orthogonal polynomials on the line and on the circle. We follow the historical development of the subject, which opens many interesting relationships of orthogonal polynomials to other important branches of mathematics. At the end we present a new formula for orthogonal polynomials on the real line, the Leganes formula, [GRAPHICS] which is a correct analogue of the corresponding formula on the unit circle. This formula is applied to obtain a recent result by Simon. (c) 2004 Elsevier B.V. All rights reserved.
Description
Khrushchev, Sergey/0000-0002-8854-5317
ORCID
Keywords
continued fraction, P-fraction, periodic fraction, Pell's equation, integration in finite terms, orthogonal polynomials, Schur's algorithm, moment's problem, periodic fraction, Schur algorithm, Continued fractions and generalizations, Orthogonal polynomials, Applied Mathematics, Integration in finite terms, Schur's algorithm, Pell's equation, integration in finite terms, Continued fraction, P-fraction, \(P\)-fraction, continued fraction, Computational Mathematics, Pell equation, moment problem, Leganés formula, Moment's problem, Convergence and divergence of continued fractions, Periodic fraction, Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis, orthogonal polynomials, Continued fractions; complex-analytic aspects
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Fields of Science
01 natural sciences, 0101 mathematics
Citation
WoS Q
Q1
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OpenCitations Citation Count
2
Source
7th International Symposium on Orthogonal Polynomials, Special Functions and Applications -- AUG 18-22, 2003 -- Univ Copenhagen, Copenhagen, DENMARK
Volume
178
Issue
1-2
Start Page
267
End Page
303
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CrossRef : 1
Scopus : 2
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2
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4
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1
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