A Numerical Investigation on the Structure of the Zeros of Euler Polynomials
Using numerical investigation, we observe the behavior of complex roots of the Euler polynomials En(x). By means of numerical experiments, we demonstrate a remarkably regular structure of the complex roots of the Euler polynomials En(x). Finally, we show the Julia set of Newton iteration function R(...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Wiley
2015-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2015/174173 |
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| _version_ | 1832548637920460800 |
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| author | C. S. Ryoo J. Y. Kang |
| author_facet | C. S. Ryoo J. Y. Kang |
| author_sort | C. S. Ryoo |
| collection | DOAJ |
| description | Using numerical investigation, we observe the behavior of complex roots of the Euler polynomials En(x). By means of numerical experiments, we demonstrate a remarkably regular structure of the complex roots of the Euler polynomials En(x). Finally, we show the Julia set of Newton iteration function R(x)=x-En(x)/En′(x). |
| format | Article |
| id | doaj-art-cebd9e6da7c74f0aa1326ea6d6b2260f |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2015-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-cebd9e6da7c74f0aa1326ea6d6b2260f2025-02-03T06:13:29ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2015-01-01201510.1155/2015/174173174173A Numerical Investigation on the Structure of the Zeros of Euler PolynomialsC. S. Ryoo0J. Y. Kang1Department of Mathematics, Hannam University, Daejeon 306-791, Republic of KoreaDepartment of Mathematics, Hannam University, Daejeon 306-791, Republic of KoreaUsing numerical investigation, we observe the behavior of complex roots of the Euler polynomials En(x). By means of numerical experiments, we demonstrate a remarkably regular structure of the complex roots of the Euler polynomials En(x). Finally, we show the Julia set of Newton iteration function R(x)=x-En(x)/En′(x).http://dx.doi.org/10.1155/2015/174173 |
| spellingShingle | C. S. Ryoo J. Y. Kang A Numerical Investigation on the Structure of the Zeros of Euler Polynomials Discrete Dynamics in Nature and Society |
| title | A Numerical Investigation on the Structure of the Zeros of Euler Polynomials |
| title_full | A Numerical Investigation on the Structure of the Zeros of Euler Polynomials |
| title_fullStr | A Numerical Investigation on the Structure of the Zeros of Euler Polynomials |
| title_full_unstemmed | A Numerical Investigation on the Structure of the Zeros of Euler Polynomials |
| title_short | A Numerical Investigation on the Structure of the Zeros of Euler Polynomials |
| title_sort | numerical investigation on the structure of the zeros of euler polynomials |
| url | http://dx.doi.org/10.1155/2015/174173 |
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