This article is cited in 1 paper

Cyclical matrices and the Chebyshev polynomials

Yu. I. Kuznetsov

Institute of Computational Mathematics and Mathematical Geophysics (Computing Center), Siberian Branch of the Russian Academy of Sciences

Abstract: A sequence of polynomials generated by a cyclical Jacobi matrix is treated as a function of an integer argument, which is the order of the polynomials. Formulas for the sum and difference of the functions and their arguments that generalize similar formulas for trigonometrical functions are constructed. An expression for such sequences of polynomials with the use of Chebyshev polynomials of the second kind is obtained. A divisibility formula for Chebyshev polynomials of the second kind is obtained. A solution of the inverse problem for Chebyshev polynomials, i.e. a description of the corresponding functions of integer arguments by using their properties is presented.

UDC: 517.518.36

Received: 23.10.2000

Bibliographic databases:

•