Some Limit Relationships Between Some Two-Variable Finite and Infinite Sequences of Orthogonal Polynomials

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2021

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Taylor & Francis Ltd

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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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Abstract

The aim of paper is to give some limit relationships between finite and infinite sequences of orthogonal polynomials in two variables and to obtain the well-known relations of some infinite sets of two-variable orthogonal polynomials by taking limit of the properties verified by finite classes of two-variable orthogonal polynomials. Furthermore, the fourth-order partial differential equations satisfied by the polynomials, which are the products of finite orthogonal polynomials, are presented and by taking limit of the derived fourth-order equations, partial differential equations for some infinite sequences of two-variable orthogonal polynomials are found.

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Güldoğan Lekesiz, Esra/0000-0001-7653-8745; Aktas, Rabia/0000-0002-7811-8610
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Güldoğan Lekesiz, Esra ORCID logo
Aktas, Rabia ORCID logo

Keywords

Orthogonal polynomial, limit relation, partial differential equation, recurrence relation, generating function

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Q3

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Q3

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Volume

27

Issue

12

Start Page

1692

End Page

1722

URI

https://doi.org/10.1080/10236198.2021.2006192
 https://hdl.handle.net/20.500.14411/1721

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