Beating Bellard's formula

By Robert Smith Fabrice Bellard came up with a computationally efficient formula for calculating the n th hexadecimal digit of $\pi$ without calculating any of the previous n −1. It&rsquo;s called Bellard&rsquo;s formula . It wasn&rsquo;t the first of its kind, but in terms of computational efficiency, it was a substantial improvement over the original, elegant Bailey-Borwein-Plouffe formula . Due…