20.500.12556/RUL-149630 Baselski problem delo diplomskega seminarja Basel problem Baselski problem, poimenovan po švicarskem mestu Basel, je že stoletja vznemirjal matematike. Gre za iskanje vsote obratnih vrednosti kvadratov naravnih števil. Le to je uspelo rešiti Eulerju, ki je pokazal, da je vsota enaka $\frac{\pi^2}{6}$. Kasneje je razširil svoje metode in znanje, da je našel zaključene oblike vsot obratnih vrednosti četrtih, šestih in drugih sodih potenc. Vendar ga te metode niso privedle do točne rešitve vsote obratnih vrednosti kubov naravnih števil. Diplomska naloga obravnava reševanje omenjenih problemov in kako je Euler poizkusil ovrednotiti vsoto obratnih vrednosti kubov, tako da jo je pretvoril v vsoto konstante in analitično neizračunljivega integrala. The Basel Problem, named after the Swiss city of Basel, has troubled mathematicians for centuries. It involves finding the sum of the reciprocals of the squares of natural numbers. Euler successfully solved this, demonstrating that the sum is $\frac{\pi^2}{6}$. Later, he expanded his methods and knowledge to find closed-form solutions for sums of reciprocals of 4th, 6th, and other even powers. However, these methods did not lead to an exact solution for the sum of the reciprocals of cubes of natural numbers. The thesis addresses the resolution of these problems and explores Euler's attempt to evaluate the sum of the reciprocals of cubes by transforming it into a sum of a constant and an analytically intractable integral. Baselski problem Zeta funkcija Apéreyeva konstanta Kubični baselski problem Basel problem Zeta function Apérey's constant Cubic Basel problem true false false Slovenski jezik Angleški jezik Delo diplomskega seminarja/zaključno seminarsko delo/naloga 2023-09-08 08:15:11 2023-09-08 08:15:13 2024-05-29 10:45:41 0000-00-00 00:00:00 2023 0 0 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 511 135495 163792643 9481.pdf 9481.pdf 1 EB0A60E44E4F36E5AD2CE184C2C824FA 43c9b2c91767383623ccfc244c206b341f30e636e1a806e05649fad8cd66d2ce 11fb1667-4e0f-11ee-9323-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=174116 Fakulteta za matematiko in fiziko 0 0 0