Some geometric series for Euler's constant
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866918534844514304 |
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| author | Burnol, Jean-François |
| author_facet | Burnol, Jean-François |
| contents | We provide representations of Euler's constant $γ=0.577...$ as series which converge geometrically fast (but use a certain sequence whose computation induces a quadratic cost). The asymptotic oscillations of these coefficients are determined to all orders. A result of independent interest, about sufficient conditions for the validity, in the case of unbounded parameters, for the Tricomi-Erdélyi asymptotic expansion of the ratio of two Gamma functions, is established for that purpose. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_29998 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Some geometric series for Euler's constant Burnol, Jean-François Number Theory Combinatorics 11Y60, 11B83, 33B15, 41A60 (Primary) 05A16, 11B68, 11M41, 30E15, 60C05 (Secondary) We provide representations of Euler's constant $γ=0.577...$ as series which converge geometrically fast (but use a certain sequence whose computation induces a quadratic cost). The asymptotic oscillations of these coefficients are determined to all orders. A result of independent interest, about sufficient conditions for the validity, in the case of unbounded parameters, for the Tricomi-Erdélyi asymptotic expansion of the ratio of two Gamma functions, is established for that purpose. |
| title | Some geometric series for Euler's constant |
| topic | Number Theory Combinatorics 11Y60, 11B83, 33B15, 41A60 (Primary) 05A16, 11B68, 11M41, 30E15, 60C05 (Secondary) |
| url | https://arxiv.org/abs/2603.29998 |