2002•Journal of Yunyang Teachers CollegeRequires access

Some Properties for Radius of Convergence of a Power Series

Zhang Ming

Abstract

Let  ∞ n=0 a nx n is a power series centered at zero with radius R of convergence. In this paper we discuss some properties about the R and introduce the general formula for the R, i.e., Cauchy-Hadamard formula:R -1 = lim n∞ sup na n By the formula we can describe how to determine the radius of new power series generated by two power series, and some examples are given.

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Key concepts: Radius of convergence, Power series, Series (stratigraphy), RADIUS, Mathematics, Convergence (economics), Hadamard transform, Zero (linguistics)