Borel's Methods of Summability Theory and Application [Hardcover]

Borel's methods of summability--transformations of one series of numbers to another--are fundamental to a whole class of sequences to function methods. Conceived at the beginning of the 20th century, they have been increasingly applied to exciting new problems in theoretical physics. Comprehensive and rigorous, this book offers an outstanding overview of the subject. It will be sought after by students and researchers in number theory.

Introduction
1. Historical Overview
2. Summability Methods in General
3. Borel's Methods of Summability
4. Relations with the Family of Circle Methods
5. Generalizations
6. Albelian Theorems
7. Tauberian Theorems--I
8. Tauberian Theorems--II
9. Relationships with Other Methods
10. Applications of Borel's Methods
References

The treatment is careful and clear throughout. The book will be a valuable work of reference in its field for many years to come. --Mathematical Reviews