缺项幂级数收敛域的求法

Study on Convergence Domain of Lacunary Power Series

求幂级数收敛域最关键的是求它的收敛半径.对于缺项(或不完全)的幂级数,由于不能直接使用教材中给出的求完全幂级数收敛半径的公式li mn→∞︱an+1an︱来求收敛半径,需要寻求新的方法.为了解决这一问题,介绍四种简单方法,先求出幂级数的收敛半径,然后考虑其收敛域.

Abstract： To find the solution of power series convergence domain, it is important to get its radius of convergence. For lacunary power series, the radius of convergence can not be computed by the formulalimn→∞｜an＋1/an｜ directly. Four new methods are proposed to work out the convergence radius and convergence domain is investigated.