Neskončne vrste in neskončni produkti : diplomsko delo

Bohinc, Silva (author), Slapar, Marko (mentor)

Osrednji del diplomskega dela je predstavitev neskončnega produkta in Wallisove formule, ki je v delu predstavljen kot zanimiv primer neskončnega produkta. Za preučevanje neskončnega produkta pa potrebujemo najprej nekaj predznanja. Uvodu bo sledilo poglavje o neskončnih vrstah; definicija neskončnih vrst, nekaj osnovne teorije o konvergenci vrst in kriterijih za ugotavljanje konvergence. Vrstam sledi poglavje o neskončnem produktu, v katerem bo predstavljen neskončni produkt in konvergenca neskončnega produkta. Za konec sledi še poglavje o Wallisovem produktu.

• Language: Slovenian
• Keywords: Wallisova formula
• Work type: Undergraduate thesis
• Typology: 2.11 - Undergraduate Thesis
• Organization: PEF - Faculty of Education
• Publisher: [S. Bohinc]
• Year: 2014
• Number of pages: 39 f.
• PID: 20.500.12556/RUL-69202
• UDC: 517.523(043.2)
• COBISS.SI-ID: 10260041
• Publication date in RUL: 10.07.2015

Secondary language

• Language: Slovenian
• Title: Infinite series and infinite products

Abstract

The main topic of my diploma thesis is the study of infinite product and the Wallis formula, which is one of the more interesting examples of infinite products. To study infinite products, we need some preliminaries. We follow the Introduction chapter with a chapter on infinite series. We give a definition of an infinite series, and present some basic results on convergence as well as a comprehensive list of convergence criteria. The next chapter is devoted to infinite products and their convergence. We conclude the thesis with a chapter on the Wallis product.