20.500.12556/DKUM-59018 Obravnava Pascalove matrike z generirajočimi funkcijami Analysis of Pascal matrix with generating functions V diplomskem delu je proučevana Pascalova matrika s pomočjo generirajočih funkcij.Prvo poglavje predstavi pojem matrika in njene zakonitosti ter računske operacije med matrikami. V drugem poglavju je opisana Pascalova matrika in nekatere njenepotence. Ta ima zelo elegantno podobo in lahko vodi do nekaterih presenetljivih rezultatov, saj predstavlja Pascalov trikotnik, ki je med najbolj slavnimi številskimi zaporedji ter je poln vzorcev. V naslednjih poglavjih pa so predstavljene generirajoče funkcije Pascalove matrike in njihove lastnosti. In this thesis the Pascal matrix is studied by means of generating functions. The first chapter introduces the concept of a matrix, it sproperties and mathematical operations on matrices. The second chapter describes the Pascal matrix and its powers. They have a very elegant appearance and can lead to some surprising results, induced by the Pascal's triangle, which is among the most famous numeric sequences and is full of patterns. In the following chapters generating functions of Pascal matrix and their properties are discused. Pascalov trikotnik Pascalova matrika eksponentna generirajoča funkcija osnovna generirajoča funkcija Pascalova matrika z dodano identiteto Pascal's triangle Pascal matrix exponential generating function basic generating function Pascal matrix with added identity. true true false [M. Garbas] Slovenski jezik Angleški jezik Diplomsko delo 2016-05-03 08:54:04 2016-09-12 12:46:11 2022-06-19 03:06:23 2019-07-11 10:59:45 2016 0 Zagorje 0 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 512.643(043.2) 22510344 URN:SI:UM:DK:MTBR4LDN UN_Garbas_Maja_2016.pdf UN_Garbas_Maja_2016.pdf 1 D6387373CCAE1904C440DBF2A921B211 4d8022212d23e0e7a48eca862d2c2c948c821e7358b7565fcd8f4fdb7c66f0c7 a1a51fa5-7c0c-11eb-bb7a-00155d0001ca https://dk.um.si/Dokument.php?lang=slv&id=93523 Fakulteta za naravoslovje in matematiko 0 0 0