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Title:Funkcija gama
Authors:ID Prešern, Tamara (Author)
ID Milutinović, Uroš (Mentor) More about this mentor... New window
Files:.pdf UNI_Presern_Tamara_2011.pdf (341,11 KB)
MD5: 3B78ED34F25AD98EB48C5EED359D8C83
PID: 20.500.12556/dkum/c57061df-27b5-44a9-b75a-f7e0974f1d7c
 
Language:Slovenian
Work type:Undergraduate thesis
Organization:FNM - Faculty of Natural Sciences and Mathematics
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:funkcija gama, funkcija beta, Stirlingova formula, konveksnost, nepravi integral, Wallisova formula
Place of publishing:Maribor
Publisher:[T. Prešern]
Year of publishing:2011
PID:20.500.12556/DKUM-19211 New window
UDC:51(043.2)
COBISS.SI-ID:18534408 New window
NUK URN:URN:SI:UM:DK:0DAWDSSD
Publication date in DKUM:18.07.2011
Views:3897
Downloads:172
Metadata:XML DC-XML DC-RDF
Categories:FNM
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Secondary language

Language:English
Title:The Gamma Function
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.
Keywords:gamma function, beta function, Stirling's formula, convexity, improper integral, Wallis formula


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