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Please somebody provide a proof in detail to this problem. I have tried it many times but no sucess so far.

Let $$ \frac{\pi\alpha} 2 = \log\tan\left( \frac \pi 4 (1+\beta) \right). $$ Then $$ \left( \frac{1^2+\alpha^2}{1^2-\beta^2} \right)\left( \frac{3^2-\beta^2}{3^2+\alpha^2} \right)^3 \left( \frac{5^2+\alpha^2}{5^2-\beta^2} \right)^5 \cdots = e^{(\pi/2)\alpha\beta}. $$

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    I would propose you take some time to formulate your question nicely (and import the LaTeX code). – 2017-01-08
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    If this was discovered by Ramanujan, it may be too challenging for everybody here. – 2017-01-08
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    @Michael Hardy i was solving his problems from published papers and got real stuck at this one – 2017-01-08
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    See p. $363$ here http://www.fuchs-braun.com/media/78bb2c662df08bdfffff8024fffffff1.pdf – 2017-01-08

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