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

Abstract

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.