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© 2017

Series of Bessel and Kummer-Type Functions

Benefits

  • 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

Book

Part of the Lecture Notes in Mathematics book series (LNM, volume 2207)

Table of contents

  1. Front Matter
    Pages i-xix
  2. Árpád Baricz, Dragana Jankov Maširević, Tibor K. Pogány
    Pages 1-25
  3. Árpád Baricz, Dragana Jankov Maširević, Tibor K. Pogány
    Pages 27-86
  4. Árpád Baricz, Dragana Jankov Maširević, Tibor K. Pogány
    Pages 87-111
  5. Árpád Baricz, Dragana Jankov Maširević, Tibor K. Pogány
    Pages 113-138
  6. Árpád Baricz, Dragana Jankov Maširević, Tibor K. Pogány
    Pages 139-184
  7. Back Matter
    Pages 185-203

About this book

Introduction

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 Fourier–Bessel series, and their manifold and polyvalent applications, mainly in general classical analysis, applied mathematics and mathematical physics.

Keywords

Fourier-Bessel Series Bessel Functions Family Integral Representations Neumann Series of Bessel Functions Family Members Kapteyn Series of Bessel Functions Family Members Kapteyn Series of Kummer Functions Schlömilch Series Dini Series Dirichlet Series Cahen Formula

Authors and affiliations

  1. 1.John von Neumann Faculty of Informatics, Institute of Applied MathematicsÓbuda UniversityBudapestHungary
  2. 2.Department of MathematicsJosip Juraj Strossmayer University of OsijekOsijekCroatia
  3. 3.Faculty of Maritime StudiesUniversity of RijekaRijekaCroatia

Bibliographic information

Reviews

“The authors of this book give an extensive study related to the series of Bessel- and Kummer-type functions. … The book also represents a solid source for master’s and PH.D. students that are starting their research careers in the field of mathematical analysis, applied mathematics and mathematical physics, to name but a few.” (Trufce Sandev, Mathematical Reviews, February, 2019)