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This is a repost from MSE as I haven’t got anything so far there. Ramanujan gave the following series evaluation $ $ 1+9\left(\frac{1}{4}\right)^{4}+17\left(\frac{1\cdot 5}{4\cdot 8}\right)^{4}+25\left(\frac{1\cdot 5\cdot 9}{4\cdot 8\cdot 12}\right)^{4}+\cdots=\dfrac{2\sqrt{2}}{\sqrt{\pi}\Gamma^{2}\left(\dfrac{3}{4}\right)}$ $ in his first and famous letter to G H Hardy. The form of the series is similar to his famous series for $ 1/\pi$ andRead more