A q-analog of Schl\"afli and Gould identities on Stirling numbers

Stirling numbers of both kinds are linked to each other via two combinatorial identities due to Schl"afli and Gould. Using q-analogs of Stirling numbers defined as inversion generating functions, we provide q-analogs of the two identities. The proof is computational and we leave open the problem of finding a more combinatorial one.