# Unproven identities

• September 21st 2007, 09:06 AM
ThePerfectHacker
Unproven identities
Does anybody know whether or not all of Ramanjuan's identities were proven? If not can you post some of them?
• September 21st 2007, 09:23 AM
Jhevon
Quote:

Originally Posted by ThePerfectHacker
Does anybody know whether or not all of Ramanjuan's identities were proven? If not can you post some of them?

nope, and no

Quote:

Signature: $\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)}
$

that's nice!