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Verižni ulomki in neskončne vrste : diplomsko delo
ID Skubic, Katja (Author), ID Slapar, Marko (Mentor) More about this mentor... This link opens in a new window, ID Starčič, Tadej (Co-mentor)

URLURL - Presentation file, Visit http://pefprints.pef.uni-lj.si/id/eprint/2464 This link opens in a new window

Abstract
V diplomskem delu bom skušala razumljivo predstaviti koncept splošnih verižnih ulomkov, njihovo povezavo s številskimi vrstami oziroma nekaterimi analitičnimi funkcijami. Pri tem si bom pobližje ogledala tudi osnovne koncepte neskončnih vrst, ustavila pa se bom tudi pri zgodovini verižnih ulomkov, saj njihovi zametki segajo daleč v zgodovino matematike in so povezani s številnimi pomembnimi matematičnimi imeni. Na koncu pa se bom posvetila še dobro znanim matematičnima konstantama, ki nas spremljata že skozi dolga stoletja. To sta števili pi in e. Raziskovanje bo namenjeno predvsem njuni predstavitvi z verižnimi ulomki ob pomoči izpeljav iz neskončnih vrst.

Language:Slovenian
Keywords:neskončni verižni ulomek, konvergenca, Taylorjeva vrsta
Work type:Bachelor thesis/paper (mb11)
Typology:2.11 - Undergraduate Thesis
Organization:PEF - Faculty of Education
Year:2014
Publisher:[K. Skubic]
Number of pages:32 str.
UDC:517.524(043.2)
COBISS.SI-ID:10216009 This link opens in a new window
Publication date in RUL:10.07.2015
Views:1109
Downloads:155
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Secondary language

Language:Slovenian
Title:Continued fractions and infinite series
Abstract:
The intention of this diploma is to present the concept of continued fractions, their conection with infinite series and some analitical functions. There will be also presented the concept of numerical series. There is a lot of history behind the continued fractions. I will only mention a few most important names which are linked with beginnings of continued fractions. At the end I will present two most known constants, numbers pi and e. I will try to write them with continued fractions using infinite series because of their close connection.


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