幂级数收敛半径的若干性质

Some Properties for Radius of Convergence of a Power Series

给出了由已知幂级数生成新的幂级数后收敛半径发生变化的若干结果 。

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.