INTRODUCTION.- CHAPTER 1: Infinite Products & Elementary Functions.- 1.1 Classical Euler representations.- 1.2 Alternative derivations.- 1.3 Other elementary functions.- 1.4 Chapter exercises.- CHAPTER 2: Green's Functions for the Laplace Equation.- 2.1 Construction by the method of images.- 2.2 Conformal mapping method.- 2.3 Chapter exercises.- CHAPTER 3: Green's Functions for ODE.- 3.1 Construction by defining properties.- 3.2 Method of variation of parameters.- 3.3 Chapter exercises.- CHAPTER 4: Method of Eigenfunction Expansion.- 4.1 Hilbert's theorem.- 4.2 Cartesian coordinates.- 4.3 Polar coordinates.- 4.4 Chapter exercises.- CHAPTER 5: New Infinite Product Representations.- 5.1 Method of images extends frontiers.- 5.2 Trigonometric functions.- 5.3 Hyperbolic functions.- 5.4 Chapter exercises.- HINTS AND ANSWERS TO CHAPTER EXERCISES.- REFERENCES.- INDEX.

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.