Has there ever been a formal proof of the following formula?

The most recent result I can find is from Bailey&Borwein (2005), who have shown that the identity holds to at least 20,000 decimal places. Yet, no proof that it is exact has been known at that time.

The Bailey&Borwein (2005) paper can be found here: http://crd-legacy.lb...math-future.pdf

Thanks,

Daniel

**Edited by renerpho, 28 September 2016 - 02:25 AM.**