Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
권호 표지
DOI QR코드

DOI QR Code

A MODIFIED POLYNOMIAL SEQUENCE OF THE CHEBYSHEV POLYNOMIALS OF THE SECOND KIND

  • Received : 2017.08.25
  • Accepted : 2017.11.21
  • Published : 2019.04.30
Download PDF
⟨ Previous Next ⟩

Abstract

Dilcher and Stolarsky [1] 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 [1], zero distribution and the irreducibility.

Keywords

References

  1. K. Dilcher and K. B. Stolarsky, Nonlinear recurrences related to Chebyshev polynomials, Ramanujan J. 41 (2016), no. 1-3, 147-169. https://doi.org/10.1007/s11139-014-9620-5
  2. J. C. Mason and D. C. Handscomb, Chebyshev Polynomials, Chapman & Hall/CRC, Boca Raton, FL, 2003.
  3. T. J. Rivlin, Chebyshev Polynomials, second edition, Pure and Applied Mathematics (New York), John Wiley & Sons, Inc., New York, 1990.