M000000361

$$\pi=82834436651472\arctan\left(\frac{1}{14483848717682}\right)-51864640759828\arctan\left(\frac{1}{15962244871097}\right)+14388350768536\arctan\left(\frac{1}{16083127751238}\right)+46568724612720\arctan\left(\frac{1}{19507778531302}\right)-34671572317260\arctan\left(\frac{1}{20293776947868}\right)-27864105223488\arctan\left(\frac{1}{28711694592682}\right)+567221591084\arctan\left(\frac{1}{31216978800818}\right)-15064247462856\arctan\left(\frac{1}{33308851938318}\right)-19709332116880\arctan\left(\frac{1}{41887379804066}\right)+16730148853860\arctan\left(\frac{1}{69971515635443}\right)-21428749127292\arctan\left(\frac{1}{83979525486773}\right)+19004697603080\arctan\left(\frac{1}{127528611030443}\right)+451169328392\arctan\left(\frac{1}{158682175700807}\right)+74122382899072\arctan\left(\frac{1}{187458398552950}\right)+31205439666728\arctan\left(\frac{1}{211773236092865}\right)+21329056201180\arctan\left(\frac{1}{240926005152903}\right)-3239393976600\arctan\left(\frac{1}{256093522057693}\right)+5471763811576\arctan\left(\frac{1}{258213230677943}\right)+38616317751780\arctan\left(\frac{1}{317335434728073}\right)-4675633249596\arctan\left(\frac{1}{370392816588001}\right)-12607377057392\arctan\left(\frac{1}{758341235653128}\right)+33267750282476\arctan\left(\frac{1}{830202489183166}\right)+52105278641120\arctan\left(\frac{1}{1143900177872158}\right)+13514275008828\arctan\left(\frac{1}{1427056404016693}\right)+13837017031856\arctan\left(\frac{1}{2270451385422943}\right)+41213339305804\arctan\left(\frac{1}{4088593248636842}\right)-8027557692432\arctan\left(\frac{1}{4161072789242257}\right)-930620955592\arctan\left(\frac{1}{4204987898062723}\right)-34500933415060\arctan\left(\frac{1}{6805164953551432}\right)+10190077024936\arctan\left(\frac{1}{7474541196075273}\right)$$

Compact formula	82834436651472[14483848717682] - 51864640759828[15962244871097] + 14388350768536[16083127751238] + 46568724612720[19507778531302] - 34671572317260[20293776947868] - 27864105223488[28711694592682] + 567221591084[31216978800818] - 15064247462856[33308851938318] - 19709332116880[41887379804066] + 16730148853860[69971515635443] - 21428749127292[83979525486773] + 19004697603080[127528611030443] + 451169328392[158682175700807] + 74122382899072[187458398552950] + 31205439666728[211773236092865] + 21329056201180[240926005152903] - 3239393976600[256093522057693] + 5471763811576[258213230677943] + 38616317751780[317335434728073] - 4675633249596[370392816588001] - 12607377057392[758341235653128] + 33267750282476[830202489183166] + 52105278641120[1143900177872158] + 13514275008828[1427056404016693] + 13837017031856[2270451385422943] + 41213339305804[4088593248636842] - 8027557692432[4161072789242257] - 930620955592[4204987898062723] - 34500933415060[6805164953551432] + 10190077024936[7474541196075273]
Lehmer's measure	2.09474
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 23 October 2006.] Download references as BibTeΧ