An equation for Gauss's constant G

 

I did some manipulations because we were dealing with Heegner number 163. I am putting two screenshots which give Gauss's constant G to 10 places.

I agree there is not much here. But for one thing. A somewhat repeated decimals. Hence 2526679/2499750.

However, I still maintain that there is a huge scope in this. And tremendous amount of learning with pi, e and G all together. Possibly going in different phases. Tough to put in one equation !!

Indians need to decide. The beauty of constants and nature in one hand !! And mathematical olympiads and problem solving on the other !!

I prefer the former. But alas most prefer the latter !!