The Lerch $Φ$ Analytic Continuation
Fuente:
arXiv
Enregistré dans:
| Auteur principal: | |
|---|---|
| Format: | Preprint |
| Publié: |
2021
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866910680826773504 |
|---|---|
| author | Sousa, Jose Risomar |
| author_facet | Sousa, Jose Risomar |
| contents | We demonstrate how to extend formulae for the Lerch transcendent function, $Φ(e^z,k,b)$, and the polylogarithm, $\mathrm{Li}_{k}(e^{z})$, that only hold at the positive integers to the right half of the complex $k$-plane, that is, $\Re{(k)}>0$. The same is done for the partial sums of each of these functions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2101_06835 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | The Lerch $Φ$ Analytic Continuation Sousa, Jose Risomar Number Theory We demonstrate how to extend formulae for the Lerch transcendent function, $Φ(e^z,k,b)$, and the polylogarithm, $\mathrm{Li}_{k}(e^{z})$, that only hold at the positive integers to the right half of the complex $k$-plane, that is, $\Re{(k)}>0$. The same is done for the partial sums of each of these functions. |
| title | The Lerch $Φ$ Analytic Continuation |
| topic | Number Theory |
| url | https://arxiv.org/abs/2101.06835 |