Identities, inequalities for Boole-type polynomials: approach to generating functions and infinite series
Abstract The main purpose and motivation of this work is to investigate and provide some new identities, inequalities and relations for combinatorial numbers and polynomials, and for Peters type polynomials with the help of their generating functions. The results of this paper involve some special n...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2019-03-01
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| Series: | Journal of Inequalities and Applications |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s13660-019-2006-x |
| _version_ | 1819208630939942912 |
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| author | Yilmaz Simsek Ji Suk So |
| author_facet | Yilmaz Simsek Ji Suk So |
| author_sort | Yilmaz Simsek |
| collection | DOAJ |
| description | Abstract The main purpose and motivation of this work is to investigate and provide some new identities, inequalities and relations for combinatorial numbers and polynomials, and for Peters type polynomials with the help of their generating functions. The results of this paper involve some special numbers and polynomials such as Stirling numbers, the Apostol–Euler numbers and polynomials, Peters polynomials, Boole polynomials, Changhee numbers and the other well-known combinatorial numbers and polynomials. Finally, in the light of Boole’s inequality (Bonferroni’s inequalities) and bounds of the Stirling numbers of the second kind, some inequalities for a combinatorial finite sum are derived. We mention an open problem including bounds for our numbers. Some remarks and observations are presented. |
| first_indexed | 2024-12-23T05:42:27Z |
| format | Article |
| id | doaj.art-720d92f61e2547d28aace1f159c74c1d |
| institution | Directory Open Access Journal |
| issn | 1029-242X |
| language | English |
| last_indexed | 2024-12-23T05:42:27Z |
| publishDate | 2019-03-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of Inequalities and Applications |
| spelling | doaj.art-720d92f61e2547d28aace1f159c74c1d2022-12-21T17:58:09ZengSpringerOpenJournal of Inequalities and Applications1029-242X2019-03-012019111110.1186/s13660-019-2006-xIdentities, inequalities for Boole-type polynomials: approach to generating functions and infinite seriesYilmaz Simsek0Ji Suk So1Department of Mathematics, Faculty of Science, University of AkdenizDepartment of Mathematics and Institute of Pure and Applied Mathematics, Chonbuk National UniversityAbstract The main purpose and motivation of this work is to investigate and provide some new identities, inequalities and relations for combinatorial numbers and polynomials, and for Peters type polynomials with the help of their generating functions. The results of this paper involve some special numbers and polynomials such as Stirling numbers, the Apostol–Euler numbers and polynomials, Peters polynomials, Boole polynomials, Changhee numbers and the other well-known combinatorial numbers and polynomials. Finally, in the light of Boole’s inequality (Bonferroni’s inequalities) and bounds of the Stirling numbers of the second kind, some inequalities for a combinatorial finite sum are derived. We mention an open problem including bounds for our numbers. Some remarks and observations are presented.http://link.springer.com/article/10.1186/s13660-019-2006-xGenerating functionFunctional equationBinomial coefficientEuler numbers and polynomialsStirling numbersPeters polynomials |
| spellingShingle | Yilmaz Simsek Ji Suk So Identities, inequalities for Boole-type polynomials: approach to generating functions and infinite series Journal of Inequalities and Applications Generating function Functional equation Binomial coefficient Euler numbers and polynomials Stirling numbers Peters polynomials |
| title | Identities, inequalities for Boole-type polynomials: approach to generating functions and infinite series |
| title_full | Identities, inequalities for Boole-type polynomials: approach to generating functions and infinite series |
| title_fullStr | Identities, inequalities for Boole-type polynomials: approach to generating functions and infinite series |
| title_full_unstemmed | Identities, inequalities for Boole-type polynomials: approach to generating functions and infinite series |
| title_short | Identities, inequalities for Boole-type polynomials: approach to generating functions and infinite series |
| title_sort | identities inequalities for boole type polynomials approach to generating functions and infinite series |
| topic | Generating function Functional equation Binomial coefficient Euler numbers and polynomials Stirling numbers Peters polynomials |
| url | http://link.springer.com/article/10.1186/s13660-019-2006-x |
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