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Generalized Mathieu Series

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Generalized Mathieu Series/ by Živorad Tomovski, Delčo Leškovski, Stefan Gerhold.
Author:	Tomovski, Živorad.
other author:	Leškovski, Delčo.
Description:	XV, 160 p. 1 illus. in color.online resource. :
Contained By:	Springer Nature eBook
Subject:	Mathematical analysis. -
Online resource:	https://doi.org/10.1007/978-3-030-84817-0
ISBN:	9783030848170

Generalized Mathieu Series
Tomovski, Živorad.

Generalized Mathieu Series[electronic resource] /by Živorad Tomovski, Delčo Leškovski, Stefan Gerhold. - 1st ed. 2021. - XV, 160 p. 1 illus. in color.online resource.

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.

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 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.

ISBN: 9783030848170

Standard No.: 10.1007/978-3-030-84817-0doiSubjects--Topical Terms:

527926
Mathematical analysis.

LC Class. No.: QA299.6-433

Dewey Class. No.: 515

Generalized Mathieu Series
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505 0 $a 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.
520 $a 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 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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