Green's Functions and Infinite Products

• 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.

From the reviews: "The book under review is an interesting textbook which is intended for students (both undergraduate and postgraduate) specializing in pure and applied mathematics. It may be considered as a good complement to standard courses in analysis and differential equations." (Konstantin Yu. Fedorovskii, Mathematical Reviews, May, 2013) "The present book provides an introduction to some recent research of the author based on a method for deriving infinite product representations for the Green's functions of the two-dimensional Laplace equation on certain domains. ... The book contains ample background material on infinite products and Green's functions ... and is, hence, accessible for graduate students. In particular, the presentation is clear and self-contained." (G. Teschl, Monatshefte fur Mathematik, Vol. 166 (3-4), June, 2012) "This book is devoted to some new infinite products for trigonometric and hyperbolic functions. ... the infinite products investigated in the book have the same speed of convergence as the classical ones. ... The book is written on a very comprehensive level and can be useful for students studying equations of mathematical physics and computer modeling." (Yana Kinderknecht, Zentralblatt MATH, Vol. 1235, 2012)