From 7c66b227a494748e2a546fb85317accd00aebe53 Mon Sep 17 00:00:00 2001 From: Justin Gassner Date: Thu, 15 Feb 2024 05:11:07 +0100 Subject: Update --- pages/complex-analysis/one-complex-variable/power-series.md | 5 +++-- 1 file changed, 3 insertions(+), 2 deletions(-) (limited to 'pages/complex-analysis/one-complex-variable/power-series.md') diff --git a/pages/complex-analysis/one-complex-variable/power-series.md b/pages/complex-analysis/one-complex-variable/power-series.md index 31793ab..4876d30 100644 --- a/pages/complex-analysis/one-complex-variable/power-series.md +++ b/pages/complex-analysis/one-complex-variable/power-series.md @@ -21,7 +21,8 @@ $a$ is the *center* of the series. {% enddefinition %} {% lemma %} -Suppose the Banach space valued power series $\sum_{n=0}^{\infty} x_n (z - a)^n$ converges for $z = a + w$. +Suppose the Banach space valued power series $\sum_{n=0}^{\infty} x_n (z - a)^n$ +converges for $z = a + w$. Then it converges absolutely for all $z$ with $\abs{z-a} < \abs{w}$. {% endlemma %} @@ -35,7 +36,7 @@ Then either - the series converges only for $z=a$ (formally $R=0$), or - there exists a number $0 R$, or - the series converges absolutely for all $z \in \CC$ (formally $R=\infty$). -- cgit v1.2.3-70-g09d2