Function Equations and Series via Differential Equations

In this book, we describe methods for solving the function equations and computing the sum of series using differential equations.At present, differential equations have become increasingly important in analyzing nature and social phenomena and solving various technological problems, and the breadth and depth of their applications are increasing.When modeling the various phenomena occurring in nature mathematically, most of them are considered as differential equations, and the methodology and computational approaches of differential equations allow quantitative and precise analysis of the engineering process of modern science and technology.Hence, it is important for mathematicians and engineers to know well the application methods of differential equations and to develop their ability to exploit them properly.What we will discuss in this book is the methodology of finding solutions of the functional equations or finding the sum of series using the solution techniques of differential equations.