LEADER 03969nam 22007455 450 001 9910510554903321 005 20250505002355.0 010 $a3-030-84817-5 024 7 $a10.1007/978-3-030-84817-0 035 $a(MiAaPQ)EBC6804999 035 $a(Au-PeEL)EBL6804999 035 $a(CKB)19422163100041 035 $a(OCoLC)1286080435 035 $a(PPN)258844612 035 $a(DE-He213)978-3-030-84817-0 035 $a(EXLCZ)9919422163100041 100 $a20211115d2021 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aGeneralized Mathieu Series /$fby ?ivorad Tomovski, Del?o Le?kovski, Stefan Gerhold 205 $a1st ed. 2021. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2021. 215 $a1 online resource (167 pages) 311 08$aPrint version: Tomovski, ?ivorad Generalized Mathieu Series Cham : Springer International Publishing AG,c2021 9783030848163 320 $aIncludes bibliographical references and index. 327 $a1 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. 330 $aThe 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. 606 $aMathematical analysis 606 $aStatistics 606 $aMathematical physics 606 $aComputer science$xMathematics 606 $aApproximation theory 606 $aFourier analysis 606 $aAnalysis 606 $aStatistical Theory and Methods 606 $aMathematical Methods in Physics 606 $aMathematics of Computing 606 $aApproximations and Expansions 606 $aFourier Analysis 615 0$aMathematical analysis. 615 0$aStatistics. 615 0$aMathematical physics. 615 0$aComputer science$xMathematics. 615 0$aApproximation theory. 615 0$aFourier analysis. 615 14$aAnalysis. 615 24$aStatistical Theory and Methods. 615 24$aMathematical Methods in Physics. 615 24$aMathematics of Computing. 615 24$aApproximations and Expansions. 615 24$aFourier Analysis. 676 $a515.54 700 $aTomovski$b Z?ivorad$0781332 702 $aGerhold$b Stefan 702 $aLes?kovski$b Delc?o 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910510554903321 996 $aGeneralized Mathieu series$92905567 997 $aUNINA