Obravnava Pascalove matrike z generirajočimi funkcijami

diplomsko delo

Maja Garbas (Author), Dušan Pagon (Mentor)

Abstract

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 njene potence. Ta ima zelo elegantno podobo in lahko vodi do nekaterih presenetljivih rezultatov, saj predstavlja Pascalov trikotnik, ki je med najbolj slavnimi številskimi zaporedji in je poln vzorcev. V naslednjih poglavjih pa so predstavljene generirajoče funkcije Pascalove matrike in njihove lastnosti.

Keywords

diplomska dela;Pascalov trikotnik;Pascalova matrika;eksponentna generirajoča funkcija;osnovna generirajoča funkcija;Pascalova matrika z dodatno funkcijo;

Data

Language:	Slovenian
Year of publishing:	2016
Typology:	2.11 - Undergraduate Thesis
Organization:	UM FNM - Faculty of Natural Sciences and Mathematics
Publisher:	[M. Garbas]
UDC:	512.643(043.2)
COBISS:	22510344
Views:	730
Downloads:	69
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	English
Secondary title:	Analysis of Pascal matrix with generating functions
Secondary abstract:	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.
Secondary keywords:	theses;Pascal's triangle;Pascal matrix;exponential generating function;basic generating function;Pascal matrix with added identity;
URN:	URN:SI:UM:
Type (COBISS):	Undergraduate thesis
Thesis comment:	Univ. v Mariboru, Fak. za naravoslovje in matematiko, Oddelek za matematiko in računalništvo
Pages:	I, 25 f.
ID:	9148931