ABSTRACT
11.1 In this chapter the definition and basic properties of a power series will be given. In particular, we will discuss various concepts of the radius of convergence of a power series, namely, the radius of uniform convergence and the radius of absolute convergence. Then we will show that a function which is represented by a power series is a C∞ function within the radius of uniform convergence. Normed spaces appearing in this chapter are vector spaces over the field https://www.w3.org/1998/Math/MathML"> K https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003065296/83108f8a-a772-47ac-b2d9-8e82b5d19535/content/ieq0195.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> .
