Examples of Power Series

In this book you find a collection of general examples of power series.

Here follows a collection of general examples of power series. The reader is also referred to Calculus 3b.

The important technique of solving linear differential equations with polynomial coefficients by means of power series is postponed to the next book in this series, Calculus 3c-4.

It should no longer be necessary rigourously to use the ADIC-model, described in Calculus 1c and Calculus 2c, because we now assume that the reader can do this himself.

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

Introduction

1. Power series; radius of convergence and sum

2. Power series expansions of functions

3. Cauchy multiplication

4. Integrals described by series

5. Sums of series