Summa summarum

by Larsen, Mogens Esrom

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Title Statements

Full title :Summa summarum / Morgens [i.e. Mogens] Esrom Larsen.

Summary

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.

Edition Statements

Publication Date:©2007.

Publication Statements

Publisher(s):A K Peters, Canadian Mathematical Society/Société mathématique du Canada
Place of Publication:Ottawa, Ont
Language:eng
Publication Date:©2007.

The Physical Object

Description:1 online resource (xii, 232 pages)

Edition Identifiers

ISBN:9781439865064, 143986506X, 9780367803711, 0367803712
DOI:10.1201/b10582
oclc:ocn682013676
LC Classification:QA246.7
Dewey Decimal:511/.6

Notation -- Elementary properties -- Polynomials -- Linear difference equations -- Classification of sums -- Gosper's algorithm -- Sums of type II(2,2,z) -- Sums of type II(3,3,z) -- Sums of type II(4,4,+1) -- Sums of type II(5,5,1) -- Other type II sums -- Zeilberger's algorithm -- Sums of types III-IV -- Sums of type V. harmonic sums -- Indefinite sums -- Basic identities.

Subjects

Analyse combinatoire Combinatorial analysis Exponential sums MATHEMATICS -- Combinatorics MATHEMATICS -- Number Theory Number theory Sommes exponentielles Théorie des nombres