Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2410.07534 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866916431599239168 |
|---|---|
| author | Kanungo, Shihan Schettler, Jordan |
| author_facet | Kanungo, Shihan Schettler, Jordan |
| contents | In this note, we evaluate a multivariable family of infinite products which generalize Guillera's infinite product for $e$, and Ser's formula (rediscovered by Sondow) for $e^γ$. We describe formulas for the products in terms of special values of the Hurwitz zeta function $ζ(s,u)$ and its $s$ derivative. Additionally, we derive integral and double integral representations for the logarithms of these infinite products. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_07534 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On Product Formulas of Guillera and Sondow Kanungo, Shihan Schettler, Jordan Number Theory 11M06, 11M35 In this note, we evaluate a multivariable family of infinite products which generalize Guillera's infinite product for $e$, and Ser's formula (rediscovered by Sondow) for $e^γ$. We describe formulas for the products in terms of special values of the Hurwitz zeta function $ζ(s,u)$ and its $s$ derivative. Additionally, we derive integral and double integral representations for the logarithms of these infinite products. |
| title | On Product Formulas of Guillera and Sondow |
| topic | Number Theory 11M06, 11M35 |
| url | https://arxiv.org/abs/2410.07534 |