  I present a partly pedagogic discussion of the Gel'fand-Yaglom formula for
the functional determinant of a one-dimensional, second order difference
operator, in the simplest settings. The formula is a textbook one in discrete
Sturm-Liouville theory and orthogonal polynomials. A two by two matrix approach
is developed and applied to Robin boundary conditions. Euler-Rayleigh sums of
eigenvalues are computed. A delta potential is introduced as a simple,
non-trivial example and extended, in an appendix, to the general case. The
continuum limit is considered in a non--rigorous way and a rough comparison
with zeta regularised values is made. Vacuum energies are also considered in
the free case. Chebyshev polynomials act as free propagators and their
properties are developed using the two-matrix formulation, which has some
advantages and appears to be novel. A trace formula, rather than a determinant
one, is derived for the Gel'fand-Yaglom function.
