On (f,b)-Determinant Sequence of the Tridiagonal Matrices and their Properties] {On (f,b)-Determinant Sequence of the Tridiagonal Matrices and their Properties

Abstract

In this paper, we introduce and study a new sequence with determinant functions, called $(f,b)$-determinant, where $f$ is a real function and $b$ a fixed real constant.
Also, we introduce a special type of the tridiagonal matrices with $f$ in the main diagonal, $b$ in the subdiagonal and we investigate the recursive pattern of their determinants. We focus on the solutions of the associated recurrence relations and the derivation of closed-form formulas. We examine different cases of tridiagonal matrices, including those with variable and constant coefficients, as well as the general solution for determinants in terms of the roots of the characteristic equations.