“circle of convergence”的概念、定义、习题解题方法及翻译-数学辞典

单词

circle of convergence

释义

circle of convergence

A circle in the complex plane such that the power series

absolutely converges for all z satisfying |z−z0|R. Here R is the radius of convergence, and if the series converges for all the complex plane then R is infinite. The disc with centre z0 and radius R is called the disc of convergence. For points on the circumference of the circle the series may either converge or diverge. These same terms apply to real power series, though the disc will in that case be an interval. The radius convergence can commonly be determined using the ratio test and in general the formula

applies (as a consequence of Cauchy's test).

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