Complex Functions Examples c-4 - Power series

This is the fourth textbook you can download containing examples from the Theory of Complex Functions. In this book we shall only consider complex power series and their relationship to the general theory.

This is the fourth book containing examples from the Theory of Complex Functions. In this volume we shall only consider complex power series and their relationship to the general theory, and finally the technique of solving linear differential equations with polynomial coefficients by means of a power series.

Even if I have tried to be careful about this text, it is impossible to avoid errors, in particular in the first edition. It is my hope that the reader will show some understanding of my situation.

Leif Mejlbro

11th June 2008

Introduction

1. Some simple theoretical results concerning power series

2. Simple Fourier series in the Theory of Complex Functions

3. Power series

4. Analytic functions described as power series

5. Linear differential equations and the power series method

6. The classical differential equations

7. Some more difficult differential equations

8. Zeros of analytic functions

9. Fourier series

10. The maximum principle