Advanced Search

We present a q-analogue of the Rhin-Viola method for the analysis of $\mathrm{\Phi }$-adic valuations of the q-gamma factors occurring in the basic Euler-Pochhammer integral representation of the Heine series $2{\varphi }_1$. Moreover, we show that this approach yields the best known irrationality measures for ${\log }_q(z)$, ${\log }_q(2)$ and ${\zeta }_q(1)$.