On the evaluation of\sum^\infty_{n=0} n^{k}x^{n}with applications to Z transforms

A particularly simple procedure for evaluating the power series
\Sum\min{n=0}\max{\infty} n^{k}x^{n}
, where
k
is a nonnegative integer, is presented. A general formula for the sum of the above series is given in which the required coefficients are obtained from a matrix which is constructed by inspection. One area of application is shown to be the evaluation of
Z
-transfer functions.