20.500.12556/RUL-162405 Računanje decimalk števila pi magistrsko delo Calculating digits of pi V delu predstavimo zgodbo števila pi. Prvi preboj pri računanju njegovih decimalk je delo Arhimeda. Po utemeljitvi infinitezimalnega računa v 17. stoletju zgodba dobi nove razsežnosti in doseže svoj vrh z iznajdbo formule bratov Chudnovsky. Ta nas popelje v svet eliptičnih in hipergeometrijskih funkcij ter kompleksnega množenja. Točnost implementacije formule lahko preverimo z BBP formulo. Za konec hipergeometrijske vrste uporabimo pri generiranju vrst za druge konstante, kar nam omogoči Zeilbergerjev algoritem. In this thesis, we present the story of the number pi. The first breakthrough in the calculation of its digits was made by Archimedes. The story gains new dimensions with the invention of infinitesimal calculus in the 17th century and reaches its climax with the discovery of Chudnovsky formula. This formula presents us with the world of elliptic and hypergeometric functions, and of complex multiplication. The correctness of the implementation can be verified with the BBP formula. We finish by using hypergeometric series to generate series for other constants, which is made possible by Zeilberger's algorithm. pi formula bratov Chudnovsky eliptične funkcije hipergeometrijske funkcije kompleksno množenje BBP formula Zeilbergerjev algoritem pi Chudnovsky formula elliptic functions hypergeometric functions complex multiplication BBP formula Zeilberger's algorithm true false false Slovenski jezik Angleški jezik Magistrsko delo/naloga 2024-09-22 08:15:18 2024-09-22 08:15:20 2024-09-26 03:21:20 0000-00-00 00:00:00 2024 0 0 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 517.5 143998 208482051 12882.pdf 12882.pdf 1 25244C96718D9BC7F114F4DBC5D590CF 1777b36d491f678a1c02c9d430e394d2d36eb65b923e73dcf5df6af188f3766d ed7e4ba7-78a9-11ef-b232-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=191719 Fakulteta za matematiko in fiziko 0 0 0