Generalized Mathieu series / Živorad Tomovski, Delčo Leškovski, Stefan Gerhold.
2021
QA405
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Title
Generalized Mathieu series / Živorad Tomovski, Delčo Leškovski, Stefan Gerhold.
Author
Tomovski, Živorad.
ISBN
9783030848170 (electronic bk.)
3030848175 (electronic bk.)
3030848167
9783030848163
3030848175 (electronic bk.)
3030848167
9783030848163
Publication Details
Cham, Switzerland : Springer, 2021.
Language
English
Description
1 online resource
Item Number
10.1007/978-3-030-84817-0 doi
Call Number
QA405
Dewey Decimal Classification
515/.54
Summary
The Mathieu series is a functional series introduced by Emile Leonard 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 Plancks distribution is 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.
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Includes bibliographical references and index.
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text file
PDF
Source of Description
Online resource; title from PDF title page (SpringerLink, viewed December 7, 2021).
Added Author
Leškovski, Delčo.
Gerhold, Stefan.
Gerhold, Stefan.
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Print version: 9783030848163
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Table of Contents
1 Introduction
2 Generalized Mathieu Series
3 Mean Convergence of Fourier-Mathieu Series
4 Estimates for Multiple Generalized Mathieu Series
5 Asymptotic Expansions of Mathieu Series
6 Two-Sided Inequalities for the Butzer-Flocke-Hauss Complete Omega Function
7 Probability Distributions Associated with Mathieu Series
8 Conclusion
Appendix A: Some special functions and their properties.
2 Generalized Mathieu Series
3 Mean Convergence of Fourier-Mathieu Series
4 Estimates for Multiple Generalized Mathieu Series
5 Asymptotic Expansions of Mathieu Series
6 Two-Sided Inequalities for the Butzer-Flocke-Hauss Complete Omega Function
7 Probability Distributions Associated with Mathieu Series
8 Conclusion
Appendix A: Some special functions and their properties.