A New Family of Orthogonal Polynomials in Three Variables

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2020

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Springer

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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

In this paper we introduce a six-parameter generalization of the four-parameter three-variable polynomials on the simplex and we investigate the properties of these polynomials. Sparse recurrence relations are derived by using ladder relations for shifted univariate Jacobi polynomials and bivariate polynomials on the triangle. Via these sparse recurrence relations, second order partial differential equations are presented. Some connection relations are obtained between these polynomials. Also, new results for the four-parameter three-variable polynomials on the simplex are given. Finally, some generating functions are derived.

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Güldoğan Lekesiz, Esra/0000-0001-7653-8745; Area, Ivan/0000-0003-0872-5017; Aktas, Rabia/0000-0002-7811-8610
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Güldoğan Lekesiz, Esra ORCID logo
Area, Ivan ORCID logo
Aktas, Rabia ORCID logo

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Jacobi polynomials, Koornwinder polynomials, Generating function, Recurrence relation, Partial differential equation, Connection relation

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2020

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1

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https://doi.org/10.1186/s13660-020-02434-5
 https://hdl.handle.net/20.500.14411/3035

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