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arXiv · 2510.19865

On Some Continued Fractions and Divergent Series Arising From Integral Families

Ishan Joshi
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Abstract

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 $\zeta(s)$, 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 $\gamma$ as the sum of a particular divergent series through a new summation method which we propose.

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Ishan Joshi. 2025-10-22. On Some Continued Fractions and Divergent Series Arising From Integral Families. https://arxiv.org/abs/2510.19865

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