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＜電子ブック＞
Generalized Mathieu Series / by Živorad Tomovski, Delčo Leškovski, Stefan Gerhold

版	1st ed. 2021.
出版者	(Cham : Springer International Publishing : Imprint: Springer)
出版年	2021
本文言語	英語
大きさ	XV, 160 p. 1 illus. in color : online resource
著者標目	*Tomovski, Živorad author Leškovski, Delčo author Gerhold, Stefan author SpringerLink (Online service)
件　名	LCSH:Mathematical analysis LCSH:Statistics  LCSH:Mathematical physics LCSH:Computer science -- Mathematics  全ての件名で検索 LCSH:Approximation theory LCSH:Fourier analysis FREE:Analysis FREE:Statistical Theory and Methods FREE:Mathematical Methods in Physics FREE:Mathematics of Computing FREE:Approximations and Expansions FREE:Fourier Analysis
一般注記	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 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 HTTP:URL=https://doi.org/10.1007/978-3-030-84817-0

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