A q-analogue of a formula of Hernandez obtained by inverting a result of Dilcher

Abstract

We prove a q-analogue of the formula ${\sum }_{1\le k\le n}\left(\genfrac{}{}{0ex}{}{n}{k}\right)(-1{)}^{k-1}{\sum }_{1\le i_1\le i_2\le ...\le i_m=k}\frac{1}{i_1{i}_2...i_m}={\sum }_{1\le k\le n}\frac{1}{k^m}$ by inverting a formula due to Dilcher.