Answer by CarP24 for Are these fast convergent series for the lemniscate...
Regarding the last section B, the gamma 1/3 cube:$$\,_2F_1\left(\frac{1}{12},\frac{7}{12};1;\frac{3^2}{253^2}\right) = \frac{253^{1/6}\,\Gamma^3\big(\tfrac{1}{3}\big)}{2\pi^2\sqrt{6}} $$where $253 =...
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[Updated on Nov.10, Dec.05.2023 and Feb.18.2024] Applying a similar approach followed in these MO questions, for Catalan's and Apery's Constants, i.e. Wilf-Zeilberger proofs starting from Dougall's...
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