An analysis on the inversion of polynomials

Abstract

In this work the application and the intervals of validity of an inverse polynomial, according to the method proposed by Arfken [1] for the inversion$^{i}$ of series, is analyzed. It is shown that, for the inverse polynomial there exists a restricted domain whose longitude depends on the magnitude of the acceptable error when the inverse polynomial is used to approximate the inverse function of the original polynomial. A method for calculating the error of the approximation and its use in determining the restricted domain is described and is fully developed up to the third order. In addition, five examples are presented where the inversion of a polynomial is applied in solving different problems encountered in basic courses on physics and mathematics. Furthermore, expressions for the eighth and ninth coefficients of a ninth-degree inverse polynomial, which are not encountered explicitly in other known references, are deduced.