Every mathematician, and user of mathematics, needs to manipulate sums or to find and handle combinatorial identities. In this book, the author provides a coherent tour of many known finite algebraic sums and offers a guide for devising simple ways of changing a given sum to a standard form that can be evaluated . As such, Summa Summarum serves as both an introduction and a reference for researchers, graduate and upper-level undergraduate students, and non-specialists alike: from tools as distinct as the most classical ideas of Euler to the recent effective computer algorithms by Gosper and Wilf-Zeilberger. The book is self-contained with relatively few prerequisites and so should be accessible to a very broad readership. This represents the first in the new Canadian Mathematical Society Treatises in Mathematics series of books: a collection of short monographs, dedicated to well defined subjects of current interest. These treatises emphasize the interdisciplinary character of the mathematical sciences and facilitate integration of methods and results from different areas of current research.
Author(s): Mogens Esrom Larsen
Publisher: A K Peters
Year: 2007
Language: English
Pages: 242
Tags: Математика;Дискретная математика;
Title
......Page 3
Contents
......Page 7
Prefaces......Page 11
1. Notation
......Page 13
2. Elementary Properties......Page 17
3. Polynomials......Page 21
4. Linear Difference Equations......Page 35
5. Classification of Sums......Page 53
6. Gosper's Algorithm......Page 65
7. Sums Type II(1,1,z)......Page 71
8. Sums of TypeII(2,2,z)......Page 75
9. Sums of TypeII(3,3,z)......Page 107
10. Sums of TypeII(4,3,-/+1)......Page 129
11. Sums of Typeii(5,5,1)......Page 139
12. Other Type II Sums......Page 145
13. Zeilberger's Algorithm......Page 157
14. Sums of Types III-IV......Page 169
15. Sums of Type V......Page 191
Appendix A. Indefinite Sums......Page 207
Appendix B. Basic Identities......Page 211
Bibliography......Page 235
Index......Page 241
