Exploring the q-Riemann zeta function and q-Bernoulli polynomials
We study that the q-Bernoulli polynomials, which were constructed by Kim, are analytic continued to βs(z). A new formula for the q-Riemann zeta function ζq(s) due to Kim in terms of nested series of ζq(n) is derived. The new concept of dynamics of the zeros of analytic continued polynomials is intr...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2005-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/DDNS.2005.171 |
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| _version_ | 1832556699130527744 |
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| author | T. Kim C. S. Ryoo L. C. Jang S. H. Rim |
| author_facet | T. Kim C. S. Ryoo L. C. Jang S. H. Rim |
| author_sort | T. Kim |
| collection | DOAJ |
| description | We study that the q-Bernoulli polynomials, which were constructed by Kim, are analytic continued to βs(z). A new formula for the q-Riemann zeta function ζq(s) due to Kim in terms of nested series of ζq(n) is derived. The new concept of dynamics of the zeros of analytic continued polynomials is introduced, and an interesting phenomenon of “scattering” of the zeros of βs(z) is observed. Following the idea of q-zeta function due to Kim, we are going to use “Mathematica” to explore a formula for ζq(n). |
| format | Article |
| id | doaj-art-a9c9d3283bc14962ab0e0aab53a63f78 |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2005-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-a9c9d3283bc14962ab0e0aab53a63f782025-02-03T05:44:39ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2005-01-012005217118110.1155/DDNS.2005.171Exploring the q-Riemann zeta function and q-Bernoulli polynomialsT. Kim0C. S. Ryoo1L. C. Jang2S. H. Rim3Science Education Research Institute, Education Science Research Center, Kongju National University, Kongju 314-701, KoreaDepartment of Mathematics, Hannam University, Daejeon 306-791, KoreaDepartment of Mathematics and Computer Science, Konkuk University, Chungcheongbuk-do, Chungju-Si 380-701, KoreaDepartment of Mathematics Education, Teachers' College Kyungpook National University, Daegu 702-701, KoreaWe study that the q-Bernoulli polynomials, which were constructed by Kim, are analytic continued to βs(z). A new formula for the q-Riemann zeta function ζq(s) due to Kim in terms of nested series of ζq(n) is derived. The new concept of dynamics of the zeros of analytic continued polynomials is introduced, and an interesting phenomenon of “scattering” of the zeros of βs(z) is observed. Following the idea of q-zeta function due to Kim, we are going to use “Mathematica” to explore a formula for ζq(n).http://dx.doi.org/10.1155/DDNS.2005.171 |
| spellingShingle | T. Kim C. S. Ryoo L. C. Jang S. H. Rim Exploring the q-Riemann zeta function and q-Bernoulli polynomials Discrete Dynamics in Nature and Society |
| title | Exploring the q-Riemann zeta function and q-Bernoulli polynomials |
| title_full | Exploring the q-Riemann zeta function and q-Bernoulli polynomials |
| title_fullStr | Exploring the q-Riemann zeta function and q-Bernoulli polynomials |
| title_full_unstemmed | Exploring the q-Riemann zeta function and q-Bernoulli polynomials |
| title_short | Exploring the q-Riemann zeta function and q-Bernoulli polynomials |
| title_sort | exploring the q riemann zeta function and q bernoulli polynomials |
| url | http://dx.doi.org/10.1155/DDNS.2005.171 |
| work_keys_str_mv | AT tkim exploringtheqriemannzetafunctionandqbernoullipolynomials AT csryoo exploringtheqriemannzetafunctionandqbernoullipolynomials AT lcjang exploringtheqriemannzetafunctionandqbernoullipolynomials AT shrim exploringtheqriemannzetafunctionandqbernoullipolynomials |