Alternative proofs of some formulas for two tridiagonal determinants

Abstract

In the paper, the authors provide five alternative proofs of two formulas for a tridiagonal determinant, supply a detailed proof of the inverse of the corresponding tridiagonal matrix, and provide a proof for a formula of another tridiagonal determinant. This is a companion of the paper [F. Qi, V. Čerňanová,and Y. S. Semenov, Some tridiagonal determinants related to central Delannoy numbers, the Chebyshev polynomials, and the Fibonacci polynomials, Politehn. Univ. Bucharest Sci. Bull. Ser. A Appl. Math. Phys. 81 (2019), in press.

Keywords

• alternative proof
• tridiagonal determinant
• tridiagonal matrix
• inverse
• primary 47b36
• secondary 11b39, 11b83,11c08, 11c20, 11y55, 15b36, 26c99