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| Format: | Preprint |
| Published: |
2025
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| Online Access: | https://arxiv.org/abs/2510.19865 |
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| _version_ | 1866912665635389440 |
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| author | Joshi, Ishan |
| author_facet | Joshi, Ishan |
| contents | In this paper we present a method to derive Eulerian continued fractions arising from a sequence of integrals. As examples, through a new derivation, we reproduce classical continued fraction expansions for the natural logarithm, the Riemann zeta function $ζ(s)$, and polylogarithms, while also obtaining several new identities. Finally, we apply the method to construct a divergent continued fraction, which provides a natural assignment of the Euler Mascheroni constant $γ$ as the sum of a particular divergent series through a new summation method which we propose. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_19865 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On Some Continued Fractions and Divergent Series Arising From Integral Families Joshi, Ishan Number Theory 40G99 (Primary) 40C99, 40A15, 11A55 (Secondary) In this paper we present a method to derive Eulerian continued fractions arising from a sequence of integrals. As examples, through a new derivation, we reproduce classical continued fraction expansions for the natural logarithm, the Riemann zeta function $ζ(s)$, and polylogarithms, while also obtaining several new identities. Finally, we apply the method to construct a divergent continued fraction, which provides a natural assignment of the Euler Mascheroni constant $γ$ as the sum of a particular divergent series through a new summation method which we propose. |
| title | On Some Continued Fractions and Divergent Series Arising From Integral Families |
| topic | Number Theory 40G99 (Primary) 40C99, 40A15, 11A55 (Secondary) |
| url | https://arxiv.org/abs/2510.19865 |