Continued Fractions and Orthogonal Polynomials on the Unit Circle

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2005

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Elsevier Science Bv

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Mathematics
(2000)
The Atılım University Department of Mathematics was founded in 2000 and it offers education in English. The Department offers students the opportunity to obtain a certificate in Mathematical Finance or Cryptography, aside from their undergraduate diploma. Our students may obtain a diploma secondary to their diploma in Mathematics with the Double-Major Program; as well as a certificate in their minor alongside their diploma in Mathematics through the Minor Program. Our graduates may pursue a career in academics at universities, as well as be hired in sectors such as finance, education, banking, and informatics. Our Department has been accredited by the evaluation and accreditation organization FEDEK for a duration of 5 years (until September 30th, 2025), the maximum FEDEK accreditation period achievable. Our Department is globally and nationally among the leading Mathematics departments with a program that suits international standards and a qualified academic staff; even more so for the last five years with our rankings in the field rankings of URAP, THE, USNEWS and WEBOFMETRIC.

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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.

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Khrushchev, Sergey/0000-0002-8854-5317
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Khrushchev, Sergey ORCID logo

Keywords

continued fraction, P-fraction, periodic fraction, Pell's equation, integration in finite terms, orthogonal polynomials, Schur's algorithm, moment's problem

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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

URI

https://doi.org/10.1016/j.cam.2004.02.027
 https://hdl.handle.net/20.500.14411/1255

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