Series of Functions

Abstract

This last chapter presents the adequate notion of convergence for sequences and series of functions, with an emphasis on the study of power series. We start by examining a power series naturally attached to an infinitely differentiable function, called its Taylor series. Then, in Sects. 11.2 and 11.3 we discuss the basic results on uniformly convergent series of functions and on power series. Finally, in Sect. 11.4, we present some applications of the theory to sequences defined by linear recurrence relations.