DOI QR코드

DOI QR Code

ON DIFFERENCE QUOTIENTS OF CHEBYSHEV POLYNOMIALS

  • Kim, Seon-Hong (Department of Mathematics Sookmyung Women's University) ;
  • Lee, Jung Hee (Department of Mathematics Sookmyung Women's University)
  • Received : 2014.07.03
  • Published : 2016.03.31

Abstract

In this paper, we investigate analytic and algebraic properties, and derive some identities satisfied by difference quotients of Chebyshev polynomials of the first kind.

Keywords

References

  1. S. Barnett, A note on the Bezoutian matrix, SIAM J. Appl. Math. 22 (1972), 84-86 https://doi.org/10.1137/0122009
  2. J. W. S. Cassels, Factorization of polynomials in several variables, in Proc. 15th Scandinavian Congress Oslo, 1968, 1-17, Springer Lecture Notes in Mathematics, 118, 1970.
  3. A. J. Engler and S. K. Khanduja, On irreducible factors of the polynomial f(x) - g(x), Internat. J. Math. 21 (2010), no. 4, 407-418. https://doi.org/10.1142/S0129167X10006082
  4. I. M. Gel'fand, M. M. Kapranov, and A. V. Zelevinsky, Discriminants, Resultants, and Multidimensional Determinants, Birkhauser, Boston, 1994.
  5. P. Lancaster and M. Tismenetsky, The Theory of Matrices with Applications, 2nd ed., Academic Press, New York, 1985.
  6. J. C. Mason and D. C. Handscomb, Chebyshev Polynomials, Chapman and Hall/CRC, Boca Raton, 2003.
  7. M. O. Rayes, V. Trevisan, and P. S. Wang, Factorization of Chebyshev Polynomials, Tech. Rep. ICM-199802-0001, Kent State University, 1998.
  8. T. J. Rivlin, Chebyshev Polynomials, From approximation theory to algebra and number theory. Pure and Applied Mathematics (New York). John Wiley and Sons, 1990.
  9. Z. H. Yang and B. F. Cui, On the Bezoutian matrix for Chebyshev polynomials, Appl. Math. Comput. 219 (2012), no. 3, 1183-1192. https://doi.org/10.1016/j.amc.2012.07.028