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This is a direct followup to the post Possible new series for $\pi$ by Timothy Chow and its numerous answers and comments. Using another formula in the same string theory paper by Saha and Sinha one ...

I am reading the article arXiv: 2207.09961, there are some interesting elliptic integrals, i.e. the formula (3.7) and (3.8). You can also see this image where $p_0(z)=\sqrt{-Q_0(z)}$ and $Q_0(z)=-\...