Communications of the
Korean Mathematical Society CKMS

ISSN(Print) 1225-1763 ISSN(Online) 2234-3024
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Commun. Korean Math. Soc. 2019; 34(2): 429-437

Online first article March 16, 2018      Printed April 30, 2019

https://doi.org/10.4134/CKMS.c170355

Copyright © The Korean Mathematical Society.

A modified polynomial sequence of the Chebyshev polynomials of the second kind

Seon-Hong Kim

Sookmyung Women's University

Abstract

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Dilcher and Stolarsky \cite{DS} recently studied a sequence resembling the Chebyshev polynomials of the first kind. In this paper, we follow their some research directions to the Chebyshev polynomials of the second kind. More specifically, we consider a sequence resembling the Chebyshev polynomials of the second kind in two different ways, and investigate its properties including relations between this sequence and the sequence studied in \cite{DS}, zero distribution and the irreducibility.

Keywords: Chebyshev polynomials of the second kind, recurrence relations, zeros

MSC numbers: Primary 30C15; Secondary 33C45

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