國立虎尾科技大學 |

Generalized Mathieu Series

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Generalized Mathieu Series/ by Živorad Tomovski, Delčo Leškovski, Stefan Gerhold.
作者:	Tomovski, Živorad.
其他作者:	Gerhold, Stefan.
面頁冊數:	XV, 160 p. 1 illus. in color.online resource. :
Contained By:	Springer Nature eBook
標題:	Fourier Analysis. -
電子資源:	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:

672627
Fourier Analysis.

LC Class. No.: QA299.6-433

Dewey Class. No.: 515

Generalized Mathieu Series
LDR:02960nam a22003975i 4500 001 1057150
003 DE-He213
005 20211115111532.0
007 cr nn 008mamaa
008 220103s2021 sz | s |||| 0|eng d
020 $a 9783030848170 $9 978-3-030-84817-0
024 7 $a 10.1007/978-3-030-84817-0 $2 doi
035 $a 978-3-030-84817-0
050 4 $a QA299.6-433
072 7 $a PBK $2 bicssc
072 7 $a MAT034000 $2 bisacsh
072 7 $a PBK $2 thema
082 0 4 $a 515 $2 23
100 1 $a Tomovski, Živorad. $e author. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 1296839
245 1 0 $a Generalized Mathieu Series $h [electronic resource] / $c by Živorad Tomovski, Delčo Leškovski, Stefan Gerhold.
250 $a 1st ed. 2021.
264 1 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2021.
300 $a XV, 160 p. 1 illus. in color. $b online resource.
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
338 $a online resource $b cr $2 rdacarrier
347 $a text file $b PDF $2 rda
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.
650 2 4 $a Fourier Analysis. $3 672627
650 2 4 $a Approximations and Expansions. $3 672153
650 2 4 $a Mathematics of Computing. $3 669457
650 2 4 $a Mathematical Methods in Physics. $3 670749
650 2 4 $a Statistical Theory and Methods. $3 671396
650 1 4 $a Analysis. $3 669490
650 0 $a Fourier analysis. $3 639284
650 0 $a Approximation theory. $3 527707
650 0 $a Computer science—Mathematics. $3 1253519
650 0 $a Physics. $3 564049
650 0 $a Statistics . $3 1253516
650 0 $a Analysis (Mathematics). $3 1253570
650 0 $a Mathematical analysis. $3 527926
700 1 $a Gerhold, Stefan. $e author. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 1362563
700 1 $a Leškovski, Delčo. $e author. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 1362562
710 2 $a SpringerLink (Online service) $3 593884
773 0 $t Springer Nature eBook
776 0 8 $i Printed edition: $z 9783030848163
776 0 8 $i Printed edition: $z 9783030848187
776 0 8 $i Printed edition: $z 9783030848194
856 4 0 $u https://doi.org/10.1007/978-3-030-84817-0
912 $a ZDB-2-SMA
912 $a ZDB-2-SXMS
950 $a Mathematics and Statistics (SpringerNature-11649)
950 $a Mathematics and Statistics (R0) (SpringerNature-43713)