Functional equation of a special Dirichlet series
In this paper we study the special Dirichlet series L(s)=23∑n=1∞sin(2πn3)n−s, s∈C This series converges uniformly in the half-plane Re(s)>1 and thus represents a holomorphic function there. We show that the function L can be extended to a holomorphic function in the whole complex-plane. The valu...
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| Format: | Article |
| Language: | English |
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Wiley
1987-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171287000462 |
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| _version_ | 1849409216490504192 |
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| author | Ibrahim A. Abou-Tair |
| author_facet | Ibrahim A. Abou-Tair |
| author_sort | Ibrahim A. Abou-Tair |
| collection | DOAJ |
| description | In this paper we study the special Dirichlet series
L(s)=23∑n=1∞sin(2πn3)n−s, s∈C
This series converges uniformly in the half-plane Re(s)>1 and thus represents a holomorphic function there. We show that the function L can be extended to a holomorphic function in the whole complex-plane. The values of the function L at the points 0,±1,−2,±3,−4,±5,… are obtained. The values at the positive integers 1,3,5,… are determined by means of a functional equation satisfied by L. |
| format | Article |
| id | doaj-art-7e56b0b0cd3e4c98bb6ea20ea7ce4791 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1987-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-7e56b0b0cd3e4c98bb6ea20ea7ce47912025-08-20T03:35:34ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251987-01-0110239540310.1155/S0161171287000462Functional equation of a special Dirichlet seriesIbrahim A. Abou-Tair0Department of Mathematics, Islamic University Gaza, Gaza- Strip, Palestinian AuthorityIn this paper we study the special Dirichlet series L(s)=23∑n=1∞sin(2πn3)n−s, s∈C This series converges uniformly in the half-plane Re(s)>1 and thus represents a holomorphic function there. We show that the function L can be extended to a holomorphic function in the whole complex-plane. The values of the function L at the points 0,±1,−2,±3,−4,±5,… are obtained. The values at the positive integers 1,3,5,… are determined by means of a functional equation satisfied by L.http://dx.doi.org/10.1155/S0161171287000462Dirichlet seriesanalytic continuationfunctional equationΓ-function. |
| spellingShingle | Ibrahim A. Abou-Tair Functional equation of a special Dirichlet series International Journal of Mathematics and Mathematical Sciences Dirichlet series analytic continuation functional equation Γ-function. |
| title | Functional equation of a special Dirichlet series |
| title_full | Functional equation of a special Dirichlet series |
| title_fullStr | Functional equation of a special Dirichlet series |
| title_full_unstemmed | Functional equation of a special Dirichlet series |
| title_short | Functional equation of a special Dirichlet series |
| title_sort | functional equation of a special dirichlet series |
| topic | Dirichlet series analytic continuation functional equation Γ-function. |
| url | http://dx.doi.org/10.1155/S0161171287000462 |
| work_keys_str_mv | AT ibrahimaaboutair functionalequationofaspecialdirichletseries |