Suppose I have an approximation $p_0/q_0$ to an irrational number $\alpha$. The hypergeometric method uses the fact that if $|Q_n\log-P_n| < C*b^{-n}$ and $|Q_n| < a^n$ then $log a/log b$ is the exponent of diophantine approximation. I'm wondering how I can determine when this is an immprovement on liouville's inequality. I know it clearly depends on the an and b, so for my question I'm looking for a and b to be given explicitly and then a description of how I might be able to determine when loga/logb is an improvement on liouville's inequality.
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