Some interesting properties and calculation of sinc integralspropertie

SungJin Kim graduated from Faculty of Mathematics, the Kim Il Sung University, and he received the M.S. degree from Faculty of Mathematics, the Kim Il Sung University in 2013. He majors in theory of complex analysis.

The sinc function is well known in people and have many interesting properties. These mathematical properties are well known in electrical engineers & physicists and used in many domains like signal processing.Since C.Stormer introduced his paper about those in 1885, many properties on sinc has been studied, generalized and results of these studies are introduced in preferences.This book is written to organize and explain the things of these properties which are studied much than others. In chapter 1, we introduce the fundamental knowledge which you need in order to understand chapter 2 and chapter 3. Here, an introduction to the series, derivative and integral of functions, Fourier transform, and our main objective, sinc function are presented.Chapter 2 describes computational methods and properties such as monotonicity, convergence of functional sequence whose integrand is a function of singular integrals, exactly what is the integral of the product of the sinc function. In the previous section of Chapter 2, we describe the uniform continuity of the sinc function.In chapter 3, we compute the sinc integral in our new and interesting way, with the method of using Fourier transform.