Does anybody know whether or not all of Ramanjuan's identities were proven? If not can you post some of them?
nope, and no
that's nice!Signature: $\displaystyle \int_0^{\infty} \frac{1 + \left( \frac{x}{b+1} \right)^2}{1+\left( \frac{x}{a} \right)^2} \cdot \frac{1+\left( \frac{x}{b+2} \right)^2}{1 + \left( \frac{x}{a+1} \right)^2} dx = \frac{1}{2^{\pi/2}}\cdot \frac{ \Gamma (a+1/2) \Gamma (b+1) \Gamma (b-a + 1/2)}{\Gamma (a) \Gamma (b+1/2) \Gamma (b-a + 1/2)}
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