M000180

$$\pi=48806264\arctan\left(\frac{1}{24208144}\right)-19619352\arctan\left(\frac{1}{54610269}\right)+18493448\arctan\left(\frac{1}{63199427}\right)+80441780\arctan\left(\frac{1}{100656977}\right)+36511268\arctan\left(\frac{1}{115453918}\right)+20970444\arctan\left(\frac{2}{322564791}\right)-9365084\arctan\left(\frac{1}{201229582}\right)+4516132\arctan\left(\frac{1}{385231007}\right)-19803492\arctan\left(\frac{1}{909140573}\right)-51401112\arctan\left(\frac{1}{1304967682}\right)+26320516\arctan\left(\frac{2}{4532659739}\right)+52802256\arctan\left(\frac{2}{4949475989}\right)+30241900\arctan\left(\frac{2}{6223926959}\right)+2115052\arctan\left(\frac{1}{18986886768}\right)-25914536\arctan\left(\frac{2}{520629831511}\right)$$
Compact formula48806264[24208144] - 19619352[54610269] + 18493448[63199427] + 80441780[100656977] + 36511268[115453918] + 20970444[322564791/2] - 9365084[201229582] + 4516132[385231007] - 19803492[909140573] - 51401112[1304967682] + 26320516[4532659739/2] + 52802256[4949475989/2] + 30241900[6223926959/2] + 2115052[18986886768] - 25914536[520629831511/2]
Lehmer's measure1.72549
References
ASN (13Jan10)(ΒΆΒΆ1.88345) (full reference coming soon)