Series of Bessel and Kummer-Type Functions

This book explores integral representations of Bessel and other special functions,including Neumann,Kapteyn,Schlömilch,Dini,and Fourier series,and provides coefficients,closed-form expressions,and summation formulas. It is intended for a mathematical audience, particularly graduate students and researchers in applied mathematics and mathematical physics.

Format: Paperback / softback
Length: 201 pages
Publication date: 25 March 2018
Publisher: Springer International Publishing AG

This comprehensive book delves into the study of a wide range of integral representations for Neumann,Kapteyn,Schlömilch,Dini, and Fourier series of Bessel and other special functions, including Struve and von Lommel functions. Its primary objective is to uncover the coefficients of the Neumann and Kapteyn series, as well as develop closed-form expressions and summation formulas for the series of Bessel functions under consideration. By employing techniques from the theory of differential equations, several integral representations are derived.

The text is specifically designed for a mathematical audience, encompassing advanced graduate students and researchers in the fields of science and mathematics who are eager to explore a fresh perspective on Fourier–Bessel series and their diverse and influential applications, particularly in the realms of general classical analysis, applied mathematics, and mathematical physics.

The book is organized into several chapters, each dedicated to exploring different aspects of the subject matter. The first chapter provides an introduction to the theory of integral representations, laying the foundation for the subsequent chapters. It discusses the historical background, fundamental concepts, and analytical tools necessary for understanding the topics covered in the book.

The second chapter focuses on the study of Neumann and Kapteyn series, which are integral representations of Bessel functions. It explores the properties, convergence criteria, and applications of these series, including their use in solving differential equations and generating special functions. The chapter also introduces the concept of hypergeometric functions and their role in the analysis of Bessel functions.

In the third chapter, the authors delve into the representation of Schlömilch and Dini series, which are integral representations of modified Bessel functions. They discuss the properties, convergence criteria, and applications of these series, including their use in solving partial differential equations and generating special functions. The chapter also introduces the concept of Laguerre polynomials and their application in the analysis of Bessel functions.

The fourth chapter focuses on the representation of Fourier series of Bessel and other special functions. It explores the properties, convergence criteria, and applications of these series, including their use in solving integral equations and generating special functions. The chapter also introduces the concept of Fourier transforms and their application in the analysis of Bessel functions.

The fifth chapter explores the application of integral representations to the study of special functions, including Struve and von Lommel functions. It discusses the properties, convergence criteria, and applications of these functions, including their use in generating infinite series and solving differential equations. The chapter also introduces the concept of Mellin transforms and their application in the analysis of special functions.

Throughout the book, numerous examples and exercises are provided to illustrate the theoretical concepts and to assist the reader in applying the techniques discussed. These examples cover a wide range of applications, including mathematical physics, engineering, and signal processing.

In conclusion, this book offers a comprehensive and up-to-date treatment of integral representations for Neumann,Kapteyn,Schlömilch,Dini, and Fourier series of Bessel and other special functions. It provides a solid foundation for advanced study in the field of mathematical analysis and its applications. By presenting the theory in a clear and concise manner, the book aims to appeal to a broad audience, including graduate students, researchers, and practitioners in the scientific community.

Weight: 354g
Dimension: 235 x 168 x 12 (mm)
ISBN-13: 9783319743493
Edition number: 1st ed. 2017