Inversion of z-transforms by solving appropriately formulated nonconstant coefficient difference equations

This note introduces a novel method for obtaining closed-form analytical solutions for the inverse
Z
-transform of functions in the class
\exp(Q(z))
with
Q(z)
a polynomial. In the application considered here, the relevant difference equation turns out to be
y(s + 1) = cy(s)+sey(s - 1), s \geq 1
, for which a complete solution is derived.