Question

نشان دهید: $$ \sum _ {n=0} ^ \infty \frac{ (-1)^{n} }{ 2^{2n}. (4n+1)^{3} } \binom{2n}{n} = \frac{ \varpi }{4 \sqrt{2} }[C+ \frac{ \pi ^{2} }{8} ] \wedge \varpi = \frac{1}{2 \sqrt{2 \pi } } \Gamma ^{2}( \frac{1}{4} ) $$

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  [1]: https://math.irancircle.com/?qa=blob&qa_blobid=17247887887552217522