Five-diagonal Toeplitz determinants and their relation to Chebyshev polynomials. (English) Zbl 0661.15006

Marr, Robert B.; Vineyard, George H.

SIAM J. Matrix Anal. Appl. 9, No. 4, 579-586 (1988).

The definition of a five-diagonal Toeplitz (5DT) determinant and the closed expressions for this determinant in terms of Chebyshev polynomials of the second kind are the subject of this paper. An explicit generating function of the 5DT determinants is also derived.

Reviewer: D.Voukalis

MSC:

15A15	Determinants, permanents, traces, other special matrix functions
15B57	Hermitian, skew-Hermitian, and related matrices
33C45	Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.)

Keywords:

five-diagonal Toeplitz determinants; Chebyshev polynomials; generating function