Un d\'eveloppement asymptotique des sommes harmoniques de Kempner-Irwin
Un d\'eveloppement asymptotique des sommes harmoniques de Kempner-Irwin
Let $I(b,d,k)$ be the subseries of the harmonic series keeping only those denominators having exactly $k$ occurrences of the digit $d$ in base $b$. We prove the existence of an asymptotic development to all orders in descending powers of $b$, for $d$ and $k$ fixed, of $I(b,d,k)-b \log(b)$ or rather, …