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MR2487690 (2010e:11063) 11J72 (11J82 33D15)
Bundschuh, Peter; Zudilin, Wadim Rational approximations to a $q$-analogue of $\pi$ and some other $q$-series. Diophantine approximation, 123–139, Dev. Math., 16, SpringerWienNewYork, Vienna, 2008.
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