Programska aplikacija za analizu asimptotskih razvoja faktorijelne funkcije

master's thesis

• Title (english): Application Program for Analysis of Asymptotic Expansions for Factorial Function
• Author: Grgur Radić
• Mentor: Tomislav Burić (mentor)
• Committee member: Tomislav Burić (predsjednik povjerenstva)
• Committee member: Lenka Mihoković (član povjerenstva)
• Committee member: Mirko Sužnjević (član povjerenstva)
• Granter: University of Zagreb; Faculty of Electrical Engineering and Computing; Zagreb
• Defense date and country: 2019-07-11, Croatia
• Scientific / art field, discipline and subdiscipline: TECHNICAL SCIENCES; Computing
• Scientific / art field, discipline and subdiscipline: TECHNICAL SCIENCES; Electrical Engineering

Abstract

Glavna tema rada je prikaz i analiza poznatih asimptotskih razvoja gama funkcije. Uz primjenu nove metode Burić-Elezović omogućeno je povezivanje i poopćavanje te poboljšanje mnogih poznatih aproksimacijskih formula Stirlingovog tipa čime su dobivene nove veoma točne aproksimacije za faktorijelnu funkciju. Prvo poglavlje je posvećeno gama funkciji te njena veza s faktorijelnom funkcijom. Također, analiziraju se Bernoullijevi polinomi. U drugom poglavlju definirani su asimptotski redovi te proučeni poznati razvoji gama funkcije Stirlingovog tipa te poopćenje i poboljšanje istih. Prezentirani su razni numerički rezultati navedenih formula. U posljednjem, trećem poglavlju, opisivat će se programska aplikacija koja je pridružena radu.

Abstract (english)

The main topic of the paper is the presentation and analysis of known asymptotic expansions of gamma function. With the application of the new Burić-Elezović method it is possible to connect, amplify and improve many known Stirling's type approximation formulas, resulting in new very accurate approximations for factorial function. The first chapter is devoted to the gamma function and its relationship to the factorial function. There are also analyzed Bernoulli's polynomials. In the second chapter, asymptotic rows were defined and studied well-known Stirling's type asymptotic expansions of the gamma function and its generalization with enhancements. Numerical results of the above formulas have been presented. In the last, third chapter, a application program that is associated with the thesis will be described.

• Keywords: gama funkcija; faktorijelna funkcija; asimptotski razvoji; Bernoullijevi brojevi; formule Stirlingovog tipa; n-pola formule; n-četvrtinske formule
• Keywords (english): gamma function; factorial function; asymptotic expansions; Bernoulli numbers; Stirling type formulas; n-half formulas; n-quarter formulas
• Language: croatian
• URN:NBN: urn:nbn:hr:168:813096
• Study programme: Title: Information and Communication Technology; Study programme type: university; Study level: graduate; Academic / professional title: magistar/magistra inženjer/inženjerka informacijske i komunikacijske tehnologije (magistar/magistra inženjer/inženjerka informacijske i komunikacijske tehnologije)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Closed access
• Created on: 2020-01-07 21:42:41