A modified polynomial sequence of the Chebyshev polynomials of the second kind
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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.
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.
참고문헌 (3)
- K. Dilcher, "Nonlinear recurrences related to Chebyshev polynomials", Ramanujan J, 41(1-3), pp.147~169 (2016)
- J. C. Mason, "Chebyshev Polynomials", pp.2003, Chapman & Hall
- T. J. Rivlin, "Chebyshev Polynomials" (1990), John Wiley & Sons, Inc