Complex Functions Examples c-7 - Applications of the Calculus of Residues

This is the seventh textbook you can download containing examples from the Theory of Complex Functions. In this volume we shall apply the calculations or residues in computing special types of trigonometric integrals, some types of improper integrals, including the computation of Cauchy’s principal value of an integral, and the sum of some types of series.

This is the seventh book containing examples from the Theory of Complex Functions. In this volume we shall apply the calculations or residues in computing special types of trigonometric integrals, some types of improper integrals, including the computation of Cauchy’s principal value of an integral, and the sum of some types of series. We shall of course assume some knowledge of the previous books and the corresponding theory.

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

19th June 2008

Introduction

1. Some practical formulæ in the applications of the calculation of residues
1.1 Trigonometric integrals
1.2 Improper integrals in general
1.3 Improper integrals, where the integrand is a rational function
1.4 Improper integrals, where the integrand is a rational function time a trigonometric function
1.5 Cauchy’s principal value
1.6 Sum of some series

2. Trigonometric integrals

3. Improper integrals in general

4. Improper integral, where the integrand is a rational function

5. Improper integrals, where the integrand is a rational function times a trigonometric function

6. Improper integrals, where the integrand is a rational function times an exponential function

7. Cauchy’s principal value

8. Sum of special types of series