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Title:
Obravnava Pascalove matrike z generirajočimi funkcijami
Authors:
ID
Garbas, Maja
(
Author
)
ID
Pagon, Dušan
(
Mentor
)
More about this mentor...
Files:
UN_Garbas_Maja_2016.pdf
(1,17 MB)
MD5: D6387373CCAE1904C440DBF2A921B211
Language:
Slovenian
Work type:
Undergraduate thesis
Typology:
2.11 - Undergraduate Thesis
Organization:
FNM - Faculty of Natural Sciences and Mathematics
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 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.
Keywords:
Pascalov trikotnik
,
Pascalova matrika
,
eksponentna generirajoča funkcija
,
osnovna generirajoča funkcija
,
Pascalova matrika z dodano identiteto
Place of publishing:
Zagorje
Publisher:
[M. Garbas]
Year of publishing:
2016
PID:
20.500.12556/DKUM-59018
UDC:
512.643(043.2)
COBISS.SI-ID:
22510344
NUK URN:
URN:SI:UM:DK:MTBR4LDN
Publication date in DKUM:
12.09.2016
Views:
1423
Downloads:
106
Metadata:
Categories:
FNM
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Secondary language
Language:
English
Title:
Analysis of Pascal matrix with generating functions
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.
Keywords:
Pascal's triangle
,
Pascal matrix
,
exponential generating function
,
basic generating function
,
Pascal matrix with added identity.
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