Some results on degenerate Daehee and Bernoulli numbers and polynomials
Abstract In this paper, we study a degenerate version of the Daehee polynomials and numbers, namely the degenerate Daehee polynomials and numbers, which were actually called the degenerate Daehee polynomials and numbers of the third kind and recently introduced by Jang et al. (J. Comput. Appl. Math....
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2020-06-01
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| Series: | Advances in Difference Equations |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s13662-020-02778-8 |
| _version_ | 1818278211370352640 |
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| author | Taekyun Kim Dae San Kim Han Young Kim Jongkyum Kwon |
| author_facet | Taekyun Kim Dae San Kim Han Young Kim Jongkyum Kwon |
| author_sort | Taekyun Kim |
| collection | DOAJ |
| description | Abstract In this paper, we study a degenerate version of the Daehee polynomials and numbers, namely the degenerate Daehee polynomials and numbers, which were actually called the degenerate Daehee polynomials and numbers of the third kind and recently introduced by Jang et al. (J. Comput. Appl. Math. 364:112343, 2020). We derive their explicit expressions and some identities involving them. Further, we introduce the multiple degenerate Daehee numbers and higher-order degenerate Daehee polynomials and numbers which can be represented in terms of integrals on the unitcube. Again, we deduce their explicit expressions and some identities related to them. |
| first_indexed | 2024-12-12T23:13:50Z |
| format | Article |
| id | doaj.art-5c9ec678156b49cfaec2cdbb749296ed |
| institution | Directory Open Access Journal |
| issn | 1687-1847 |
| language | English |
| last_indexed | 2024-12-12T23:13:50Z |
| publishDate | 2020-06-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Advances in Difference Equations |
| spelling | doaj.art-5c9ec678156b49cfaec2cdbb749296ed2022-12-22T00:08:31ZengSpringerOpenAdvances in Difference Equations1687-18472020-06-012020111310.1186/s13662-020-02778-8Some results on degenerate Daehee and Bernoulli numbers and polynomialsTaekyun Kim0Dae San Kim1Han Young Kim2Jongkyum Kwon3School of Science, Xian Technological UniversityDepartment of Mathematics, Sogang UniversityDepartment of Mathematics, Kwangwoon UniversityDepartment of Mathematics Education and ERI, Gyeongsang National UniversityAbstract In this paper, we study a degenerate version of the Daehee polynomials and numbers, namely the degenerate Daehee polynomials and numbers, which were actually called the degenerate Daehee polynomials and numbers of the third kind and recently introduced by Jang et al. (J. Comput. Appl. Math. 364:112343, 2020). We derive their explicit expressions and some identities involving them. Further, we introduce the multiple degenerate Daehee numbers and higher-order degenerate Daehee polynomials and numbers which can be represented in terms of integrals on the unitcube. Again, we deduce their explicit expressions and some identities related to them.http://link.springer.com/article/10.1186/s13662-020-02778-8Degenerate Daehee polynomials and numbersMultiple degenerate Daehee numbersHigher-order degenerate Daehee polynomials and numbers |
| spellingShingle | Taekyun Kim Dae San Kim Han Young Kim Jongkyum Kwon Some results on degenerate Daehee and Bernoulli numbers and polynomials Advances in Difference Equations Degenerate Daehee polynomials and numbers Multiple degenerate Daehee numbers Higher-order degenerate Daehee polynomials and numbers |
| title | Some results on degenerate Daehee and Bernoulli numbers and polynomials |
| title_full | Some results on degenerate Daehee and Bernoulli numbers and polynomials |
| title_fullStr | Some results on degenerate Daehee and Bernoulli numbers and polynomials |
| title_full_unstemmed | Some results on degenerate Daehee and Bernoulli numbers and polynomials |
| title_short | Some results on degenerate Daehee and Bernoulli numbers and polynomials |
| title_sort | some results on degenerate daehee and bernoulli numbers and polynomials |
| topic | Degenerate Daehee polynomials and numbers Multiple degenerate Daehee numbers Higher-order degenerate Daehee polynomials and numbers |
| url | http://link.springer.com/article/10.1186/s13662-020-02778-8 |
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