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Question Number 136757 by Dwaipayan Shikari last updated on 25/Mar/21

$$1+{\left(\frac{1}{2}\right)}^2\frac{1}{2.1!}+{\left(\frac{1.3}{2^2}\right)}^2\frac{1}{2^2.2!}+\left(\frac{1.3.5}{2^3}\right).\frac{1}{2^3.3!}+....={\left(\frac{\mathrm{\Gamma }\left(\frac{1}{4}\right)}{{\left(2{\pi }^3\right)}^{1/4}}\right)}^2$$

Answered by mindispower last updated on 25/Mar/21

$$1+\sum _{n⩾1}\frac{\underset{k=0}{\prod ^{n-1}}{(2k+1)}^2}{2^{3n}.n!}...?$$$$$$

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