20.500.12556/DKUM-17605 Baselski problem The Basel problem V zgodovini se je mnogo matematikov posvetilo reševanju problemov neskončnih vrst. Prve velike korake na tem področju je zagotovo naredil eden slavnejših matematikov Euler, ki je prvi heuristično dokazal, da je točna vrednost vsote obratnih kvadratov pozitivnih naravnih števil enaka pi na kvadrat šestin. Omenjena enakost je danes bolj poznana pod imenom Baselski problem, katerega različni dokazi so prikazani v tem diplomskem delu. Poleg Eulerjevega dokaza zgoraj navedene enakosti so se skozi zgodovino na področju matematične analize pojavljali vedno novi in novi dokazi. Nekateri izmed teh dokazov so predstavljeni v diplomskem delu. V literaturi je mogoče zaslediti, da je Baselski problem aktualen še danes in da se bodo zato novi dokazi najverjetneje pojavljali tudi v bodoče. Many mathematicians studied solving problems about infinity series in history. First great step in this field was made by one of the most famous mathematicians Euler, who proved that sum of inverse quadratic values of positive natural numbers is equal to square of pi divided by six, using heuristic methods. Today, his identity is called the Basel problem and different proofs of it are presented in this Graduation Thesis. Besides Euler’s proof of above identity, other new proofs based on mathematical analysis were made in history. Some of this proofs are presented in this Graduation Thesis. In literature it is possible to find that the topic of the Basel problem is still state of the art and for this reason it can be expected that new proofs will be made in the future work. matematična analiza Baselski problem vrste trigonometrija dvojni integrali mathematical analysis Basel problem series trigonometry double integral. true true false [M. Kompolšek] Slovenski jezik Angleški jezik Diplomsko delo 2011-02-28 22:13:36 2011-03-10 12:42:51 2022-04-13 09:38:54 2023-12-22 03:38:31 2011 0 Maribor 0 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 51(043.2) 18204936 URN:SI:UM:DK:PWGBLLWG UNI_Kompolsek_Melita_2011.pdf UNI_Kompolsek_Melita_2011.pdf 1 55EEF76AC21C5E4FA713A482406657D4 89b53b2e58fe99902385319a10bb78f92bdada9d81c55c64c2b990db985f88a8 eec2ea87-7c04-11eb-bb7a-00155d0001ca 20.500.12556/dkum/a5f41dea-fccc-4e2f-8f3a-13d1a0f5d0d0 https://dk.um.si/Dokument.php?lang=slv&id=20628 Fakulteta za naravoslovje in matematiko 0 0 0