These are two famous identities of Ramanujan. Where can I find the proofs of them:
$ \displaystyle \frac{1}{\pi} = \frac{2\sqrt{2}}{9801} \sum\limits_{k=0}^{\infty} \frac{(4k!)(1103 + 26390k)}{(k!)^{2} (396)^{4k}}$
$\displaystyle \int\limits_{0}^{\infty} \frac{1 + x^{2}/(b+1)^{2}}{1+x^{2}/a^{2}} \times \frac{1+ x^{2}/(b+2)^{2}}{1 + x^{2}/(a+1)^{2}} \times \cdots dx= \frac{\sqrt{\pi}}{2} \times \frac{\Gamma(a+1) \Gamma(b+\frac{1}{2}) \Gamma(b-a+\frac{1}{2}}{\Gamma(a)\Gamma(b+\frac{1}{2} \Gamma(b-a+1)}$ for $0 < a < b+\frac{1}{2}$.