The Zeta and Related Functions: Recent Developments
The main object of this survey-cum-expository article is to present an overview of some recent developments involving the Riemann Zeta function ζ(s), the Hurwitz (or generalized) Zeta function ζ(s, a), and the Hurwitz-Lerch Zeta function Φ(z, s, a), which have their roots in the works of the great e...
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| Format: | Article |
| Language: | English |
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Ton Duc Thang University
2019-03-01
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| Series: | Journal of Advanced Engineering and Computation |
| Online Access: | http://jaec.vn/index.php/JAEC/article/view/229 |
| _version_ | 1818039219611762688 |
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| author | H. M. Srivastava |
| author_facet | H. M. Srivastava |
| author_sort | H. M. Srivastava |
| collection | DOAJ |
| description | The main object of this survey-cum-expository article is to present an overview of some recent developments involving the Riemann Zeta function ζ(s), the Hurwitz (or generalized) Zeta function ζ(s, a), and the Hurwitz-Lerch Zeta function Φ(z, s, a), which have their roots in the works of the great eighteenth-century Swiss mathematician, Leonhard Euler (1707–1783) and the Russian mathematician, Christian Goldbach (1690–1764). We aim at considering the problems associated with the evaluations and representations of ζ(s) when s ∈ N \ {1}, N is the set of natural numbers, with emphasis upon several interesting classes of rapidly convergent series representations for ζ(2n+1) (n ∈ N). Symbolic and numerical computations using Mathematica (Version 4.0) for Linux will also be provided for supporting their computational usefulness.
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium provided the original work is properly cited. |
| first_indexed | 2024-12-10T07:55:09Z |
| format | Article |
| id | doaj.art-73b8f515f9f149d392eef4616f348240 |
| institution | Directory Open Access Journal |
| issn | 1859-2244 2588-123X |
| language | English |
| last_indexed | 2024-12-10T07:55:09Z |
| publishDate | 2019-03-01 |
| publisher | Ton Duc Thang University |
| record_format | Article |
| series | Journal of Advanced Engineering and Computation |
| spelling | doaj.art-73b8f515f9f149d392eef4616f3482402022-12-22T01:56:56ZengTon Duc Thang UniversityJournal of Advanced Engineering and Computation1859-22442588-123X2019-03-013132935410.25073/jaec.201931.22987The Zeta and Related Functions: Recent DevelopmentsH. M. Srivastava0UVic Department of Mathematics and StatisticsThe main object of this survey-cum-expository article is to present an overview of some recent developments involving the Riemann Zeta function ζ(s), the Hurwitz (or generalized) Zeta function ζ(s, a), and the Hurwitz-Lerch Zeta function Φ(z, s, a), which have their roots in the works of the great eighteenth-century Swiss mathematician, Leonhard Euler (1707–1783) and the Russian mathematician, Christian Goldbach (1690–1764). We aim at considering the problems associated with the evaluations and representations of ζ(s) when s ∈ N \ {1}, N is the set of natural numbers, with emphasis upon several interesting classes of rapidly convergent series representations for ζ(2n+1) (n ∈ N). Symbolic and numerical computations using Mathematica (Version 4.0) for Linux will also be provided for supporting their computational usefulness. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium provided the original work is properly cited.http://jaec.vn/index.php/JAEC/article/view/229 |
| spellingShingle | H. M. Srivastava The Zeta and Related Functions: Recent Developments Journal of Advanced Engineering and Computation |
| title | The Zeta and Related Functions: Recent Developments |
| title_full | The Zeta and Related Functions: Recent Developments |
| title_fullStr | The Zeta and Related Functions: Recent Developments |
| title_full_unstemmed | The Zeta and Related Functions: Recent Developments |
| title_short | The Zeta and Related Functions: Recent Developments |
| title_sort | zeta and related functions recent developments |
| url | http://jaec.vn/index.php/JAEC/article/view/229 |
| work_keys_str_mv | AT hmsrivastava thezetaandrelatedfunctionsrecentdevelopments AT hmsrivastava zetaandrelatedfunctionsrecentdevelopments |