M000000239

$$\pi=2069272524\arctan\left(\frac{1}{1479406293}\right)+5914859172\arctan\left(\frac{1}{5760773543}\right)+3065285204\arctan\left(\frac{1}{6608082112}\right)-4944109940\arctan\left(\frac{1}{18710140581}\right)+4863957212\arctan\left(\frac{2}{37954184589}\right)+6120983256\arctan\left(\frac{1}{24858161060}\right)-1665912812\arctan\left(\frac{1}{29546599818}\right)+7225662824\arctan\left(\frac{2}{112899039159}\right)-1353663992\arctan\left(\frac{2}{113079487129}\right)+1804057220\arctan\left(\frac{1}{70753148211}\right)+1853171256\arctan\left(\frac{1}{94111829193}\right)-3584923384\arctan\left(\frac{1}{102416588812}\right)-4958600840\arctan\left(\frac{1}{113201494333}\right)+3141084772\arctan\left(\frac{1}{265542904947}\right)-3994869308\arctan\left(\frac{1}{378137211957}\right)-4278794900\arctan\left(\frac{1}{3737240479718}\right)-1954868664\arctan\left(\frac{1}{5720348475587}\right)+2213013600\arctan\left(\frac{1}{8256835333313}\right)-1250066084\arctan\left(\frac{1}{10041983931693}\right)-225105876\arctan\left(\frac{1}{11830545643782}\right)$$

Compact formula	2069272524[1479406293] + 5914859172[5760773543] + 3065285204[6608082112] - 4944109940[18710140581] + 4863957212[37954184589/2] + 6120983256[24858161060] - 1665912812[29546599818] + 7225662824[112899039159/2] - 1353663992[113079487129/2] + 1804057220[70753148211] + 1853171256[94111829193] - 3584923384[102416588812] - 4958600840[113201494333] + 3141084772[265542904947] - 3994869308[378137211957] - 4278794900[3737240479718] - 1954868664[5720348475587] + 2213013600[8256835333313] - 1250066084[10041983931693] - 225105876[11830545643782]
Lehmer's measure	1.81293
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 17 August 2003.] Download references as BibTeΧ