# Green's Functions and Infinite Products

## Bridging the Divide

• Yuri A. Melnikov
Textbook

1. Front Matter
Pages I-X
2. Yuri A. Melnikov
Pages 1-15
3. Yuri A. Melnikov
Pages 17-42
4. Yuri A. Melnikov
Pages 43-60
5. Yuri A. Melnikov
Pages 61-83
6. Yuri A. Melnikov
Pages 85-120
7. Yuri A. Melnikov
Pages 121-149
8. Yuri A. Melnikov
Pages 151-158
9. Back Matter
Pages 159-165

### Introduction

This textbook accounts for two seemingly unrelated mathematical topics drawn from two separate areas of mathematics that have no evident points of contiguity. Green's function is a topic in partial differential equations and covered in most standard texts, while infinite products are used in mathematical analysis. For the two-dimensional Laplace equation, Green's functions are conventionally constructed by either the method of images, conformal mapping, or the eigenfunction expansion. The present text focuses on the construction of Green's functions for a wide range of boundary-value problems.

Green's Functions and Infinite Products provides a thorough introduction to the classical subjects of the construction of Green's functions for the two-dimensional Laplace equation and the infinite product representation of elementary functions.  Every chapter begins with a review guide, outlining the basic concepts covered. A set of carefully designed challenging exercises is available at the end of each chapter to provide the reader with the opportunity to explore the concepts in more detail. Hints, comments, and answers to most of those exercises can be found at the end of the text. In addition, several illustrative examples are offered at the end of most sections. This text is intended for an elective graduate course or seminar within the scope of either pure or applied mathematics.

### Keywords

Classical Euler representations Conformal mapping method Eigenfunction Expansion Hilbert's theorem Infinite Product Representations Method of images Method of variation

#### Authors and affiliations

• Yuri A. Melnikov
• 1
1. 1., Department of Mathematical SciencesMiddle Tennessee State UniversityMurfreesboroUSA