Where can I locate the evidence of the adhering to identifications of Ramanujan

These are 2 renowned identifications of Ramanujan . Where can I locate the evidence of them :

  1. $ \displaystyle \frac{1}{\pi} = \frac{2\sqrt{2}}{9801} \sum\limits_{k=0}^{\infty} \frac{(4k!)(1103 + 26390k)}{(k!)^{2} (396)^{4k}}$

  2. $\displaystyle \int\limits_{0}^{\infty} \frac{1 + x^{2}/(b+1)^{2}}{1+x^{2}/a^{2}} \times \frac{1+ x^{2}/(b+2)^{2}}{1 + x^{2}/(a+1)^{2}} \times \cdots dx= \frac{\sqrt{\pi}}{2} \times \frac{\Gamma(a+1) \Gamma(b+\frac{1}{2}) \Gamma(b-a+\frac{1}{2}}{\Gamma(a)\Gamma(b+\frac{1}{2} \Gamma(b-a+1)}$ for $0 < a < b+\frac{1}{2}$.

2019-05-07 15:01:46
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Answers: 1

Since you appear to be in Chennai, stroll right into any kind of maths collection and also grab the accumulated jobs of Ramanujan. That is the most effective. Or check into the notes modified by Bruce Berndt.

2019-05-09 10:45:28