- #1
Goongyae
- 70
- 0
Not sure if this interests anyone (maybe it's too basic?), but
pi = (5^1.25/2) * (2/sqrt(5)) * (3/sqrt(10)) * (5/sqrt(25)) * (7/sqrt(50)) * (11/sqrt(120)) * ...
Each radicand is the square of the corresponding prime number numerator, but rounded to the nearest mutliple of 5.
I derived this by evaluating the Dirchlet function with character (1,-1,-1,1,0), basically 1 - 2^-2 - 3^-2 + 4^-2 + 6^-2 -7^-2 -8^-2 +9^-2 +...
pi = (5^1.25/2) * (2/sqrt(5)) * (3/sqrt(10)) * (5/sqrt(25)) * (7/sqrt(50)) * (11/sqrt(120)) * ...
Each radicand is the square of the corresponding prime number numerator, but rounded to the nearest mutliple of 5.
I derived this by evaluating the Dirchlet function with character (1,-1,-1,1,0), basically 1 - 2^-2 - 3^-2 + 4^-2 + 6^-2 -7^-2 -8^-2 +9^-2 +...