Home page People Seminars Polski

2011-06-14 Seminarium

Last edit

Changed:

< //**Uwaga:** seminarium odbędzie się w sali A1-33 (sala posiedzeń Rady Wydziału.//

to

> //**Uwaga:** seminarium odbędzie się w sali **A1-33** (sala posiedzeń Rady Wydziału o godzinie **9.00**.//


Xiao-Xiong Gan
(Mathematics Department, Morgan State University, Baltimore, USA)

Formal Power Series and the Boundary Convergence of Power Series

Uwaga: seminarium odbędzie się w sali A1-33 (sala posiedzeń Rady Wydziału o godzinie 9.00.

The behaviour of power series on boundary of convergence domain has been an interesting topic since power series was introduced. For example,

$$  f(x) = \sum_{n=1}^{\infty}\dfrac{(-1)^n}{n}x^n $$

converges on $$ (-1,1] $$ but diverges at $$ x = -1 $$, and $$  f^{\prime}(x)  $$ diverges at both $$ x = 1 $$ and $$ x = -1 $$. The composition of formal power series has been an important part of the formal power series theory. We introduce some relationship between these two subjects and provide a condition for convergence of a power series at every point in its interval of convergence, including endpoints or boundary points.