Generalized Mathieu Series

By: Delco Leskovski, Zivorad Tomovski, Stefan Gerhold

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Hardcover | 16 November 2021

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Hardcover
178 Pages

Dimensions(cm)
23.5 x 15.5 x 1.12

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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 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.

Industry Reviews

"The authors discuss in great detail integral representations, series representations and inequalities for various classes of generalized Mathieu series. Asymptotic expansions of these Mathieu series, ... relations of generalized Mathieu series and probability theory are the main topics related to the generalized Mathieu series discussed in this well written book. The book is of interest for researchers of classical analysis working in the field of special functions or inequalities for functions defined on the real axis." (âªrp¡d Baricz, Mathematical Reviews, December, 2022)

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