M000000301

$$\pi=\frac{710423007324}{5}\arctan\left(\frac{2}{181932669739}\right)+\frac{5108337564}{5}\arctan\left(\frac{1}{148431551771}\right)+\frac{332682086048}{5}\arctan\left(\frac{1}{168722145007}\right)+\frac{469564255676}{5}\arctan\left(\frac{1}{202954204459}\right)+\frac{509033308472}{5}\arctan\left(\frac{1}{221943811240}\right)+\frac{35127438388}{5}\arctan\left(\frac{1}{250645741818}\right)+39977727128\arctan\left(\frac{1}{261217252912}\right)+\frac{299079800424}{5}\arctan\left(\frac{1}{269007136889}\right)+\frac{212853724728}{5}\arctan\left(\frac{1}{548275361132}\right)\frac{-468612987024}{5}\arctan\left(\frac{1}{662573197307}\right)\frac{-144943461156}{5}\arctan\left(\frac{1}{1372432573478}\right)\frac{-134901320908}{5}\arctan\left(\frac{1}{2105653391693}\right)-49699840956\arctan\left(\frac{1}{3761284561432}\right)+\frac{51284385576}{5}\arctan\left(\frac{1}{5142102426318}\right)\frac{-711399462252}{5}\arctan\left(\frac{1}{5745192731179}\right)+63463938620\arctan\left(\frac{2}{13078246979509}\right)\frac{-457996721136}{5}\arctan\left(\frac{1}{8589803519307}\right)\frac{-376129635828}{5}\arctan\left(\frac{1}{10892900268195}\right)\frac{-189310613624}{5}\arctan\left(\frac{1}{17780261434697}\right)-83437496688\arctan\left(\frac{1}{25331597869589}\right)+\frac{210742572164}{5}\arctan\left(\frac{1}{165171481279982}\right)+\frac{286775226856}{5}\arctan\left(\frac{1}{169838669284032}\right)\frac{-517057184692}{5}\arctan\left(\frac{1}{1948025182233307}\right)+\frac{163379287796}{5}\arctan\left(\frac{1}{1976865441422893}\right)$$

Compact formula	710423007324/5[181932669739/2] + 5108337564/5[148431551771] + 332682086048/5[168722145007] + 469564255676/5[202954204459] + 509033308472/5[221943811240] + 35127438388/5[250645741818] + 39977727128[261217252912] + 299079800424/5[269007136889] + 212853724728/5[548275361132] - 468612987024/5[662573197307] - 144943461156/5[1372432573478] - 134901320908/5[2105653391693] - 49699840956[3761284561432] + 51284385576/5[5142102426318] - 711399462252/5[5745192731179] + 63463938620[13078246979509/2] - 457996721136/5[8589803519307] - 376129635828/5[10892900268195] - 189310613624/5[17780261434697] - 83437496688[25331597869589] + 210742572164/5[165171481279982] + 286775226856/5[169838669284032] - 517057184692/5[1948025182233307] + 163379287796/5[1976865441422893]
Lehmer's measure	1.93261
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 08 August 2006.] Download references as BibTeΧ