diplomsko delo
Tamara Prešern (Author), Uroš Milutinović (Mentor)

Abstract

Osrednja tema diplomskega dela je funkcija gama. Definiramo jo z nepravim integralom in dokažemo njene osnovne karakteristike. Dokažemo tudi izrek, ki opisuje pogoje, ki funkcijo gama enolično določajo. Nato še definiramo funkcijo beta in navedemo nekaj osnovnih lastnosti in povezav med funkcijama beta in gama. Na koncu še izpeljemo Stirlingove formule in s pomočjo le-teh dokažemo Wallisovo formulo.

Keywords

matematika;funkcija gama;funkcija beta;Stirlingova formula;konveksnost;nepravi integral;Wallisova formula;diplomska dela;

Data

Language: Slovenian
Year of publishing:
Source: Maribor
Typology: 2.11 - Undergraduate Thesis
Organization: UM FNM - Faculty of Natural Sciences and Mathematics
Publisher: [T. Prešern]
UDC: 51(043.2)
COBISS: 18534408 Link will open in a new window
Views: 2881
Downloads: 135
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Other data

Secondary language: English
Secondary title: The Gamma Function
Secondary abstract: The main theme of this graduation thesis is the gamma function. We define it with the improper integral and prove its basic characteristics. We also prove the theorem stating certain conditions that uniquely determine the function gamma. Then we define the beta function, state its main characteristics, and show some connections between the functions beta and gamma. At the end we derive the Stirling's formulas and with the help of these prove the Wallis formula.
Secondary keywords: gamma function;beta function;Stirling's formula;convexity;improper integral;Wallis formula;
URN: URN:SI:UM:
Type (COBISS): Undergraduate thesis
Thesis comment: Univ. v Mariboru, Fak. za naravoslovje in matematiko, Oddelek za matematiko in računalništvo
Pages: 45 f.
Keywords (UDC): mathematics;natural sciences;naravoslovne vede;matematika;mathematics;matematika;
ID: 19391
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