Advanced Engineering Mathematics, 7th Edition

19.2 Taylor Series

INTRODUCTION

The correspondence between a complex number z within the circle of convergence and the number to which the series converges is single-valued. In this sense, a power series defines or represents a function f; for a specified z within the circle of convergence, the number L to which the power series converges is defined to be the value of f at z; that is, f(z) = L. In this section we present some important facts about the nature of this function f.

In the preceding section we saw that every power series has a radius of convergence R. Throughout the discussion in this section, we will assume that a power series ...