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

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1 Author(s)
H. Abed ; Lebanese University, Beirut, Lebanon

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.

Published in:

IEEE Transactions on Automatic Control  (Volume:17 ,  Issue: 6 )