M000000322

$$\pi=262746996846\arctan\left(\frac{1}{1017929209281}\right)+1169537617469\arctan\left(\frac{2}{2554491928011}\right)+1535033301198\arctan\left(\frac{1}{1356392695807}\right)+679307286857\arctan\left(\frac{1}{2057093978843}\right)-236223059987\arctan\left(\frac{1}{2292939666693}\right)+3673776799323\arctan\left(\frac{1}{2423153939240}\right)-2651642139680\arctan\left(\frac{2}{6646491492891}\right)+115439704218\arctan\left(\frac{1}{3419484435037}\right)+434815427292\arctan\left(\frac{1}{5142102426318}\right)-2148302742458\arctan\left(\frac{1}{16883072401443}\right)-2204997925798\arctan\left(\frac{1}{18104444568932}\right)-386233195566\arctan\left(\frac{2}{43777069138111}\right)-384592078373\arctan\left(\frac{1}{27224803284193}\right)+13706716424\arctan\left(\frac{1}{35527561593282}\right)+255840717189\arctan\left(\frac{2}{78034472049011}\right)+1759754166072\arctan\left(\frac{1}{45773351286993}\right)+801565719034\arctan\left(\frac{1}{74305247702057}\right)-621151631076\arctan\left(\frac{1}{79090959114159}\right)+1894820313643\arctan\left(\frac{1}{84251069013553}\right)-1988451073050\arctan\left(\frac{1}{159493341500663}\right)-439187363240\arctan\left(\frac{1}{162768495532807}\right)-470020129551\arctan\left(\frac{1}{169838669284032}\right)-653864351073\arctan\left(\frac{1}{229180244713453}\right)+1142438226123\arctan\left(\frac{1}{526264109797943}\right)+1268743156989\arctan\left(\frac{1}{903521917122898}\right)-738812610764\arctan\left(\frac{1}{1427056404016693}\right)+922328760062\arctan\left(\frac{1}{9505680304081018}\right)$$

Compact formula	262746996846[1017929209281] + 1169537617469[2554491928011/2] + 1535033301198[1356392695807] + 679307286857[2057093978843] - 236223059987[2292939666693] + 3673776799323[2423153939240] - 2651642139680[6646491492891/2] + 115439704218[3419484435037] + 434815427292[5142102426318] - 2148302742458[16883072401443] - 2204997925798[18104444568932] - 386233195566[43777069138111/2] - 384592078373[27224803284193] + 13706716424[35527561593282] + 255840717189[78034472049011/2] + 1759754166072[45773351286993] + 801565719034[74305247702057] - 621151631076[79090959114159] + 1894820313643[84251069013553] - 1988451073050[159493341500663] - 439187363240[162768495532807] - 470020129551[169838669284032] - 653864351073[229180244713453] + 1142438226123[526264109797943] + 1268743156989[903521917122898] - 738812610764[1427056404016693] + 922328760062[9505680304081018]
Lehmer's measure	2.01039
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 06 August 2006.] Download references as BibTeΧ