**Translations of Mathematical Monographs**

1984;
286 pp;
Softcover

MSC: Primary 05;
Secondary 32

Print ISBN: 978-0-8218-4512-7

Product Code: MMONO/59

List Price: $104.00

AMS Member Price: $83.20

MAA Member Price: $93.60

**Electronic ISBN: 978-1-4704-4473-0
Product Code: MMONO/59.E**

List Price: $104.00

AMS Member Price: $83.20

MAA Member Price: $93.60

# Integral Representation and the Computation of Combinatorial Sums

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*G. P. Egorychev*

This monograph should be of interest to a broad spectrum of readers: specialists in discrete and continuous mathematics, physicists, engineers, and others interested in computing sums and applying complex analysis in discrete mathematics. It contains investigations on the problem of finding integral representations for and computing finite and infinite sums (generating functions); these arise in practice in combinatorial analysis, the theory of algorithms and programming on a computer, probability theory, group theory, and function theory, as well as in physics and other areas of knowledge. A general approach is presented for computing sums and other expressions in closed form by reducing them to one-dimensional and multiple integrals, most often to contour integrals.

#### Table of Contents

# Table of Contents

## Integral Representation and the Computation of Combinatorial Sums

- Cover Cover11
- Title page iii4
- Contents v6
- Foreword ix10
- Introduction 112
- 1. The method of integral representation of combinatorial sums 920
- 2. Integral representation and computation of one-dimensional combinatorial sums 4354
- 3. Inversion and classification of linear relations in combinatorial analysis 8798
- 4. Combinatorial interpretation, integral representation, and estimation of certain sums in combinatorial analysis 111122
- 5. Integral representation and computation of multi-dimensional sums 149160
- 6. Applications 187198
- 7. Open problems 223234
- Supplement: Facts from the Theory of Multidimensional Residues 229240
- Appendix: Table M. Integral Representations of Numbers 269280
- bibliography 275286
- Subject index 285296
- Back Cover Back Cover1299