Overview
- Gives an overview of the research based on Mathieu series
- Provides cases of asymptotic expansions of Mathieu series
- Addressed at graduate and PhD students and researchers in mathematics and physics
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Table of contents (6 chapters)
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Front Matter
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Back Matter
Keywords
About this book
The Mathieu series is a functional series introduced by Émile Léonard Mathieu for the purposes of his research on the elasticity of solid bodies. Bounds for this series are needed for solving biharmonic equations in a rectangular domain. In addition to Tomovski and his coauthors, Pogany, Cerone, H. M. Srivastava, J. Choi, etc. are some of the known authors who published results concerning the Mathieu series, its generalizations and their alternating variants. Applications of these results are given in classical, harmonic and numerical analysis, analytical number theory, special functions, mathematical physics, probability, quantum field theory, quantum physics, etc. Integral representations, analytical inequalities, asymptotic expansions and behaviors of some classes of Mathieu series are presented in this book. A systematic study of probability density functions and probability distributions associated with the Mathieu series, its generalizations and Planck’s distributionis also presented. The book is addressed at graduate and PhD students and researchers in mathematics and physics who are interested in special functions, inequalities and probability distributions.
Reviews
Authors and Affiliations
About the authors
Stefan Gerhold is a full professor in the research unit of financial and actuarial mathematics, TU Wien, Austria. He holds a PhD from Johannes Kepler University, Linz and has published approximately 50 papers in peer-reviewed journals. His main research interests are mathematical finance and probability theory, with a focus on asymptotic methods, as well as special functions and symbolic computation.
Delčo Leškovski is an assistant professor at International Balkan University, Republic of North Macedonia. His research interests include mathematical analysis, special functions, Mathieu series, probability and statistics and differential equations. He is an author or coauthor of several articles in mathematical peer-reviewed journals.
Živorad Tomovski has held the position of full professor since 2010 at the Ss. Cyril and Methodius University of Skopje, North Macedonia. He held visiting researcher positions at many prestigious universities and research institutes across Europe. Since 2021, he has been an associate professor of applied analysis and probability and statistics at the University of Ostrava, Czech Republic. He has published 1 Springer book and over 100 international papers in the areas of pure and applied mathematics.
Bibliographic Information
Book Title: Generalized Mathieu Series
Authors: Živorad Tomovski, Delčo Leškovski, Stefan Gerhold
DOI: https://doi.org/10.1007/978-3-030-84817-0
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021
Hardcover ISBN: 978-3-030-84816-3Published: 16 November 2021
Softcover ISBN: 978-3-030-84819-4Published: 17 November 2022
eBook ISBN: 978-3-030-84817-0Published: 15 November 2021
Edition Number: 1
Number of Pages: XV, 160
Number of Illustrations: 1 illustrations in colour
Topics: Analysis, Statistical Theory and Methods, Mathematical Methods in Physics, Mathematics of Computing, Approximations and Expansions, Fourier Analysis