Application of Chebyschev Polynomial to Economization of Power Series

Abstract

The truncated power series of the continuous function f(x) will not generally be a good approximate due to great error it possesses, however the error may be reduced by making n so large so as to include many terms. But the cost of evaluating large number of terms is high; it is often possible to reduce considerably the necessary number of terms without increasing the error significantly, this is the feature that allows economization. In this paper a better power series representations of functions by Chebyschev polynomials to economize Maclaurin series is sought for. The procedure is tested on two functions.