An approximation of the Hurwitz zeta function by a finite sum
We obtain the following version of the approximation of the Hurwitz zeta-function. Let σ ≥ 0 and |t| ≤ π x. Then ζ(s, α) = ∑0 ≤ n ≤ x 1/(n + α)s +{ (x + α)1−s}/(s − 1) + Θ ({7√2π−1 + 3}/xσ).
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| Format: | Article |
| Language: | English |
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Vilnius University Press
2003-12-01
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| Series: | Lietuvos Matematikos Rinkinys |
| Online Access: | https://www.journals.vu.lt/LMR/article/view/32314 |
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| _version_ | 1832593167704129536 |
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| author | Ramūnas Garunkštis |
| author_facet | Ramūnas Garunkštis |
| author_sort | Ramūnas Garunkštis |
| collection | DOAJ |
| description |
We obtain the following version of the approximation of the Hurwitz zeta-function. Let σ ≥ 0 and |t| ≤ π x. Then
ζ(s, α) = ∑0 ≤ n ≤ x 1/(n + α)s +{ (x + α)1−s}/(s − 1) + Θ ({7√2π−1 + 3}/xσ).
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| format | Article |
| id | doaj-art-ffeb55206ce64fae81e6ffb90ca03ef5 |
| institution | Kabale University |
| issn | 0132-2818 2335-898X |
| language | English |
| publishDate | 2003-12-01 |
| publisher | Vilnius University Press |
| record_format | Article |
| series | Lietuvos Matematikos Rinkinys |
| spelling | doaj-art-ffeb55206ce64fae81e6ffb90ca03ef52025-01-20T18:18:05ZengVilnius University PressLietuvos Matematikos Rinkinys0132-28182335-898X2003-12-0143spec.10.15388/LMR.2003.32314An approximation of the Hurwitz zeta function by a finite sumRamūnas Garunkštis0Vilnius University We obtain the following version of the approximation of the Hurwitz zeta-function. Let σ ≥ 0 and |t| ≤ π x. Then ζ(s, α) = ∑0 ≤ n ≤ x 1/(n + α)s +{ (x + α)1−s}/(s − 1) + Θ ({7√2π−1 + 3}/xσ). https://www.journals.vu.lt/LMR/article/view/32314 |
| spellingShingle | Ramūnas Garunkštis An approximation of the Hurwitz zeta function by a finite sum Lietuvos Matematikos Rinkinys |
| title | An approximation of the Hurwitz zeta function by a finite sum |
| title_full | An approximation of the Hurwitz zeta function by a finite sum |
| title_fullStr | An approximation of the Hurwitz zeta function by a finite sum |
| title_full_unstemmed | An approximation of the Hurwitz zeta function by a finite sum |
| title_short | An approximation of the Hurwitz zeta function by a finite sum |
| title_sort | approximation of the hurwitz zeta function by a finite sum |
| url | https://www.journals.vu.lt/LMR/article/view/32314 |
| work_keys_str_mv | AT ramunasgarunkstis anapproximationofthehurwitzzetafunctionbyafinitesum AT ramunasgarunkstis approximationofthehurwitzzetafunctionbyafinitesum |