Some identities for generalized Chebyshev polynomials

Abstract

We consider special linear combinations of classical Chebyshev polynomials (of the 2nd kind) generating a class of polynomials related to “local perturbations” of the coefficients of the discrete Schrödinger equation. These polynomials are called the generalized Chebyshev polynomials. Namely, we find an explicit expression of the coefficients of this linear combination (connection coefficients) using the coefficients of the recurrence relations defining generalized Chebyshev polynomials. This report is a continuation of authors’ work [1].