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arXiv · 2301.06495

Transcendence of some infinite series

Fedoua Sghiouer·Kacem Belhroukia·Ali Kacha
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Abstract

In the present paper and as an application of Roth's theorem concerning the rational approximation of algebraic numbers, we give a sufficient condition that will assure us that a series of positive rational terms is a transcendental number. With the same conditions, we establish a transcendental measure of $ \sum_{n = 1}^{\infty} 1/a_n$.

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Fedoua Sghiouer, Kacem Belhroukia, Ali Kacha. 2023-01-16. Transcendence of some infinite series. https://arxiv.org/abs/2301.06495

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