Complex Analysis

5

Sequence and Series

5.1 INTRODUCTION

In Chapter 2, we have studied about the definition and convergence of the sequence with the help of limit. Now, in this chapter, we will study about the sequence and series representation of analytic function in detail and prove the existence of such representation with the help of some theorems. Further, we will also study about the power series, its absolute and uniform convergence followed by term by term differentiation and integration.

5.2 CONVERGENCE OF SEQUENCE

A sequence {z_n} is said to converge to z₀ (when n approaches ∞), if for any ε > 0, there exists a positive integer N such that

 

|z_n − z₀| < ε    whenever n ≥ N

Symbolically,

A sequence which is not convergent is called divergent sequence. ...