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Richa Nandra, Lovely Professional University Unit 8: Series

Unit 8: Series Notes

CONTENTS
Objectives

Introduction
8.1 Sequences
8.2 Series
8.3 Power Series
8.4 Integration of Power Series

8.5 Differentiation of Power Series
8.6 Summary
8.7 Keywords

8.8 Self Assessment
8.9 Review Questions
8.10 Further Readings

Objectives

After studying this unit, you will be able to:
Define sequences

Discuss series and power series

Describe integration by power series

Explain differentiation by power series

Introduction

In earlier unit, you have studied about concept of transformation and conformal mapping.
In this unit, we shall introduce you to series representation of a complex valued function f (z) .
In order to obtain and analyze these series, we need to develop some concepts related to series.
We shall start the unit by discussing basic facts regarding the convergence of sequences and
series of complex numbers.

8.1 Sequences

The basic definitions for complex sequences and series are essentially the same as for the real
case. A sequence of complex numbers is a function g : Z  C from the positive integers into the
+
complex numbers. It is traditional to use subscripts to indicate the values of the function. Thus,
we write g(n)  z and an explicit name for the sequence is seldom used; we write simply (z ) to
n
n

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