# Where can I find the proofs of the following identities of Ramanujan

These are two famous identities of Ramanujan. Where can I find the proofs 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 $0 < a < b+\frac{1}{2}$.

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Consider adding some specifics to your title, maybe "Where can I find the proofs of the following identities of Ramanujan?" Long titles show up very well on the main page. – Tom Stephens Aug 9 '10 at 19:45
mathdl.maa.org/images/upload_library/22/Hasse/… may be of use (I don't understand what machinery they use but it claims to prove the series) it also says the full details are in 'Pi and the AGM: a study in the analytic number theory and computational complexity'. – anon Aug 9 '10 at 22:19
Hurrah! Motivation! – Charles Stewart Aug 10 '10 at 12:45