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