Series of Bessel and Kummer-Type Functions

This book is devoted to the study of certain integral representations for Neumann, Kapteyn, Schlömilch, Dini and Fourier series of Bessel and other special functions, such as Struve and von Lommel functions. The aim is also to find the coefficients of the Neumann and Kapteyn series, as well as closed-form expressions and summation formulas for the series of Bessel functions considered. Some integral representations are deduced using techniques from the theory of differential equations.

The text is aimed at a mathematical audience, including graduate students and those in the scientific community who are interested in a new perspective on FourierBessel series, and their manifold and polyvalent applications, mainly in general classical analysis, applied mathematics and mathematical physics.

Features novel mathematical tools and ideas which complement those in the classical theory of special functions Includes results on Bessel and Kummer type series which are applicable to problems in mathematical physics Contains an exhaustive list of references and links to further literature

Inhalt

1. Introduction and Preliminaries.- 2. Neumann Series.- 3. Kapteyn Series.- 4. Schlomilch Series.- 5. Miscellanea.