Sum of the Hurwitz-Lerch Zeta Function over Natural Numbers: Derivation and Evaluation
We consider a Hurwitz-Lerch zeta function Φs,z,a sum over the natural numbers. We provide an analytically continued closed form solution for this sum in terms of the addition of Hurwitz-Lerch zeta functions. A new recurrence identity with consecutive neighbours and the product of trigonometric funct...
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| Format: | Article |
| Language: | English |
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Wiley
2022-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2022/3591775 |
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| _version_ | 1832554964338081792 |
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| author | Robert Reynolds Allan Stauffer |
| author_facet | Robert Reynolds Allan Stauffer |
| author_sort | Robert Reynolds |
| collection | DOAJ |
| description | We consider a Hurwitz-Lerch zeta function Φs,z,a sum over the natural numbers. We provide an analytically continued closed form solution for this sum in terms of the addition of Hurwitz-Lerch zeta functions. A new recurrence identity with consecutive neighbours and the product of trigonometric functions is derived. |
| format | Article |
| id | doaj-art-73d1a0a386b3404da1da9d8d3506270b |
| institution | Kabale University |
| issn | 2314-4785 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-73d1a0a386b3404da1da9d8d3506270b2025-02-03T05:50:00ZengWileyJournal of Mathematics2314-47852022-01-01202210.1155/2022/3591775Sum of the Hurwitz-Lerch Zeta Function over Natural Numbers: Derivation and EvaluationRobert Reynolds0Allan Stauffer1Department of Mathematics and StatisticsDepartment of Mathematics and StatisticsWe consider a Hurwitz-Lerch zeta function Φs,z,a sum over the natural numbers. We provide an analytically continued closed form solution for this sum in terms of the addition of Hurwitz-Lerch zeta functions. A new recurrence identity with consecutive neighbours and the product of trigonometric functions is derived.http://dx.doi.org/10.1155/2022/3591775 |
| spellingShingle | Robert Reynolds Allan Stauffer Sum of the Hurwitz-Lerch Zeta Function over Natural Numbers: Derivation and Evaluation Journal of Mathematics |
| title | Sum of the Hurwitz-Lerch Zeta Function over Natural Numbers: Derivation and Evaluation |
| title_full | Sum of the Hurwitz-Lerch Zeta Function over Natural Numbers: Derivation and Evaluation |
| title_fullStr | Sum of the Hurwitz-Lerch Zeta Function over Natural Numbers: Derivation and Evaluation |
| title_full_unstemmed | Sum of the Hurwitz-Lerch Zeta Function over Natural Numbers: Derivation and Evaluation |
| title_short | Sum of the Hurwitz-Lerch Zeta Function over Natural Numbers: Derivation and Evaluation |
| title_sort | sum of the hurwitz lerch zeta function over natural numbers derivation and evaluation |
| url | http://dx.doi.org/10.1155/2022/3591775 |
| work_keys_str_mv | AT robertreynolds sumofthehurwitzlerchzetafunctionovernaturalnumbersderivationandevaluation AT allanstauffer sumofthehurwitzlerchzetafunctionovernaturalnumbersderivationandevaluation |