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arXiv · 2404.13763

On the asymptotics of Kempner-Irwin sums

Jean-François Burnol
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Abstract

Let $I(b,d,k)$ be the subseries of the harmonic series keeping the integers having exactly $k$ occurrences of the digit $d$ in base $b$. We prove the existence of an asymptotic expansion to all orders in descending powers of $b$, for fixed $d$ and $k$, of $I(b,d,k)-b\log(b)$. We explicitly give, depending on cases, either four or five terms. The coefficients involve the values of the zeta function at the integers.

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Jean-François Burnol. 2024-04-21. On the asymptotics of Kempner-Irwin sums. https://doi.org/10.1142/s1793042126501319

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