M000306

$$\pi=11220\arctan\left(\frac{1}{5257}\right)-1592\arctan\left(\frac{1}{9466}\right)+7800\arctan\left(\frac{1}{12943}\right)+7400\arctan\left(\frac{1}{34208}\right)+8084\arctan\left(\frac{1}{44179}\right)+8388\arctan\left(\frac{1}{85353}\right)+5936\arctan\left(\frac{1}{114669}\right)+5556\arctan\left(\frac{1}{330182}\right)+3232\arctan\left(\frac{1}{485298}\right)$$
Compact formula11220[5257] - 1592[9466] + 7800[12943] + 7400[34208] + 8084[44179] + 8388[85353] + 5936[114669] + 5556[330182] + 3232[485298]
Lehmer's measure1.95678
References
GAUSS (1863)(ΒΆΒΆ2.29361) (full reference coming soon)