Geodesic
q-Hypergeometric Functions and Irrationality Measures
Bollettino della Unione matematica italiana, Série 9, Tome 3 (2010) no. 1, pp. 137-148.

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We present a q-analogue of the Rhin-Viola method for the analysis of $\Phi$-adic valuations of the q-gamma factors occurring in the basic Euler-Pochhammer integral representation of the Heine series $2\phi_{1}$. Moreover, we show that this approach yields the best known irrationality measures for $\log_{q}(z)$, $\log_{q}(2)$ and $\zeta_{q}(1)$. 
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Merilä, Ville. q-Hypergeometric Functions and Irrationality Measures. Bollettino della Unione matematica italiana, Série 9, Tome 3 (2010) no. 1, pp. 137-148. http://geodesic.mathdoc.fr/item/BUMI_2010_9_3_1_a5/

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