Аннотация:In the paper, the authors give a motivation from central Delannoy numbers to
a tridiagonal determinant, find a generating function for the tridiagonal determinant,
prove several formulas for the tridiagonal determinant, discuss the inverse of the tridiagonal matrix, connect the tridiagonal determinant with the Chebyshev polynomials,
the Fibonacci numbers and polynomials, and the Cauchy product of central Delannoy
numbers, derive several formulas for the tridiagonal determinant and the second kind
Chebyshev polynomials, review computation of general tridiagonal determinants, present
two new formulas for computing general tridiagonal determinants, and generalize central
Delannoy numbers and their Cauchy product.