Existence of infinite series for $\ln(π)$

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We all know there are lots of series representations for $π$.

But here I want to know if there exists an infinite series for $\lnπ$.

We can get obvious one from Wallis formula ( in terms of logs).

Also, I know the following series

\begin{align} \ln(1+(7\pi/22-1)) & = -\sum_{n=1}^\infty\frac{(-1)^n}{n}(7\pi/22-1)^n \end{align}

But, I want to know is there a 'simpler' one with rational terms with may be few dealable irrational terms?