A Note on the 𝑞-Euler Numbers and Polynomials with Weak Weight 𝛼
We construct a new type of 𝑞-Euler numbers and polynomials with weak weight 𝛼 : 𝐸(𝛼)𝑛,𝑞, 𝐸(𝛼)𝑛,𝑞(𝑥), respectively. Some interesting results and relationships are obtained. Also, we observe the behavior of roots of the 𝑞-Euler numbers 𝐸(𝛼)𝑛,𝑞 and polynomials 𝐸(𝛼)𝑛,𝑞(𝑥) with weak weight 𝛼. By means of...
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| Format: | Article |
| Language: | English |
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Wiley
2011-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2011/497409 |
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| author | H. Y. Lee N. S. Jung C. S. Ryoo |
| author_facet | H. Y. Lee N. S. Jung C. S. Ryoo |
| author_sort | H. Y. Lee |
| collection | DOAJ |
| description | We construct a new type of 𝑞-Euler numbers and polynomials with weak weight 𝛼 : 𝐸(𝛼)𝑛,𝑞, 𝐸(𝛼)𝑛,𝑞(𝑥), respectively. Some interesting results and relationships are obtained. Also, we observe the behavior of roots of the 𝑞-Euler numbers 𝐸(𝛼)𝑛,𝑞 and polynomials 𝐸(𝛼)𝑛,𝑞(𝑥) with weak weight 𝛼. By means of numerical experiments, we demonstrate a remarkably regular structure of the complex roots of 𝑞-Euler polynomials 𝐸(𝛼)𝑛,𝑞 with weak weight 𝛼. |
| format | Article |
| id | doaj-art-9f55b1647fa444a2a5c0c0815f2d1d81 |
| institution | OA Journals |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2011-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-9f55b1647fa444a2a5c0c0815f2d1d812025-08-20T02:20:30ZengWileyJournal of Applied Mathematics1110-757X1687-00422011-01-01201110.1155/2011/497409497409A Note on the 𝑞-Euler Numbers and Polynomials with Weak Weight 𝛼H. Y. Lee0N. S. Jung1C. S. Ryoo2Department of Mathematics, Hannam University, Daejeon 306-791, Republic of KoreaDepartment of Mathematics, Hannam University, Daejeon 306-791, Republic of KoreaDepartment of Mathematics, Hannam University, Daejeon 306-791, Republic of KoreaWe construct a new type of 𝑞-Euler numbers and polynomials with weak weight 𝛼 : 𝐸(𝛼)𝑛,𝑞, 𝐸(𝛼)𝑛,𝑞(𝑥), respectively. Some interesting results and relationships are obtained. Also, we observe the behavior of roots of the 𝑞-Euler numbers 𝐸(𝛼)𝑛,𝑞 and polynomials 𝐸(𝛼)𝑛,𝑞(𝑥) with weak weight 𝛼. By means of numerical experiments, we demonstrate a remarkably regular structure of the complex roots of 𝑞-Euler polynomials 𝐸(𝛼)𝑛,𝑞 with weak weight 𝛼.http://dx.doi.org/10.1155/2011/497409 |
| spellingShingle | H. Y. Lee N. S. Jung C. S. Ryoo A Note on the 𝑞-Euler Numbers and Polynomials with Weak Weight 𝛼 Journal of Applied Mathematics |
| title | A Note on the 𝑞-Euler Numbers and Polynomials with Weak Weight 𝛼 |
| title_full | A Note on the 𝑞-Euler Numbers and Polynomials with Weak Weight 𝛼 |
| title_fullStr | A Note on the 𝑞-Euler Numbers and Polynomials with Weak Weight 𝛼 |
| title_full_unstemmed | A Note on the 𝑞-Euler Numbers and Polynomials with Weak Weight 𝛼 |
| title_short | A Note on the 𝑞-Euler Numbers and Polynomials with Weak Weight 𝛼 |
| title_sort | note on the 𝑞 euler numbers and polynomials with weak weight 𝛼 |
| url | http://dx.doi.org/10.1155/2011/497409 |
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