M000000244

$$\pi=2069272524\arctan\left(\frac{1}{1479406293}\right)+1250066084\arctan\left(\frac{1}{4038832337}\right)+8240836784\arctan\left(\frac{1}{9561488343}\right)+1702255108\arctan\left(\frac{1}{18471834623}\right)+5031693368\arctan\left(\frac{1}{18710140581}\right)-1156975624\arctan\left(\frac{1}{24139206772}\right)+1887350516\arctan\left(\frac{1}{24858161060}\right)+8558245428\arctan\left(\frac{1}{37017669307}\right)-149054688\arctan\left(\frac{2}{112899039159}\right)-3969251908\arctan\left(\frac{1}{71354040503}\right)+7515144132\arctan\left(\frac{1}{102416588812}\right)-3557723312\arctan\left(\frac{1}{113201494333}\right)-444388848\arctan\left(\frac{1}{225891903693}\right)-6266812012\arctan\left(\frac{1}{374583684956}\right)-4811130764\arctan\left(\frac{1}{378137211957}\right)-2381115936\arctan\left(\frac{1}{1053586529897}\right)-553991136\arctan\left(\frac{1}{2554104718836}\right)+2832864600\arctan\left(\frac{1}{3737240479718}\right)+3388785252\arctan\left(\frac{1}{3931260155877}\right)-5391262816\arctan\left(\frac{1}{28148191112477}\right)$$

Compact formula	2069272524[1479406293] + 1250066084[4038832337] + 8240836784[9561488343] + 1702255108[18471834623] + 5031693368[18710140581] - 1156975624[24139206772] + 1887350516[24858161060] + 8558245428[37017669307] - 149054688[112899039159/2] - 3969251908[71354040503] + 7515144132[102416588812] - 3557723312[113201494333] - 444388848[225891903693] - 6266812012[374583684956] - 4811130764[378137211957] - 2381115936[1053586529897] - 553991136[2554104718836] + 2832864600[3737240479718] + 3388785252[3931260155877] - 5391262816[28148191112477]
Lehmer's measure	1.81958
References	Wetherfield, Michael Roby and Chien-Lih, Hwang. Computing pi: Lists of Machin-type (inverse cotangent) identities for pi/4, [Online; accessed 04-February-2024], 2013. [web.archive.org/web/20240204042153/http] [Found by MRW on 22 January 2004.] Download references as BibTeΧ