M000000288

$$\pi=\frac{472353390728}{5}\arctan\left(\frac{1}{121409547033}\right)+\frac{273539330488}{5}\arctan\left(\frac{1}{138873731225}\right)+\frac{110996578872}{5}\arctan\left(\frac{1}{202954204459}\right)+\frac{569310248968}{5}\arctan\left(\frac{1}{218123852367}\right)\frac{-347719321352}{5}\arctan\left(\frac{1}{250645741818}\right)\frac{-40578051456}{5}\arctan\left(\frac{1}{261002206018}\right)+\frac{926844360408}{5}\arctan\left(\frac{1}{261217252912}\right)+\frac{414703271992}{5}\arctan\left(\frac{1}{269007136889}\right)+\frac{938441515636}{5}\arctan\left(\frac{1}{548275361132}\right)+\frac{403857761856}{5}\arctan\left(\frac{1}{656902304557}\right)+\frac{1185658041536}{5}\arctan\left(\frac{1}{1372432573478}\right)+\frac{415920242872}{5}\arctan\left(\frac{1}{1944056438568}\right)\frac{-1089868197264}{5}\arctan\left(\frac{1}{3761284561432}\right)\frac{-210326432988}{5}\arctan\left(\frac{1}{5142102426318}\right)+\frac{331508021756}{5}\arctan\left(\frac{2}{13078246979509}\right)\frac{-378549035268}{5}\arctan\left(\frac{1}{8589803519307}\right)+\frac{177353967504}{5}\arctan\left(\frac{1}{10892900268195}\right)+\frac{924232274588}{5}\arctan\left(\frac{1}{17780261434697}\right)\frac{-145987346996}{5}\arctan\left(\frac{1}{38759264489343}\right)+\frac{64608274812}{5}\arctan\left(\frac{1}{169838669284032}\right)\frac{-742624640396}{5}\arctan\left(\frac{1}{342036110675693}\right)+\frac{605486034668}{5}\arctan\left(\frac{1}{772654028018543}\right)+\frac{315074086692}{5}\arctan\left(\frac{1}{1948025182233307}\right)\frac{-300597684548}{5}\arctan\left(\frac{1}{1976865441422893}\right)$$

Compact formula	472353390728/5[121409547033] + 273539330488/5[138873731225] + 110996578872/5[202954204459] + 569310248968/5[218123852367] - 347719321352/5[250645741818] - 40578051456/5[261002206018] + 926844360408/5[261217252912] + 414703271992/5[269007136889] + 938441515636/5[548275361132] + 403857761856/5[656902304557] + 1185658041536/5[1372432573478] + 415920242872/5[1944056438568] - 1089868197264/5[3761284561432] - 210326432988/5[5142102426318] + 331508021756/5[13078246979509/2] - 378549035268/5[8589803519307] + 177353967504/5[10892900268195] + 924232274588/5[17780261434697] - 145987346996/5[38759264489343] + 64608274812/5[169838669284032] - 742624640396/5[342036110675693] + 605486034668/5[772654028018543] + 315074086692/5[1948025182233307] - 300597684548/5[1976865441422893]
Lehmer's measure	1.91689
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 18 September 2004.] Download references as BibTeΧ