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master's thesis
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Special functions
Dino Škrobar (2016)
Josip Juraj Strossmayer University of Osijek
Department of Mathematics
Chair of Pure Mathematics
Algebra and Calculus Research Group
Cite this document

Škrobar, D. (2016). Specijalne funkcije (Master's thesis). Retrieved from https://urn.nsk.hr/urn:nbn:hr:126:313983

Škrobar, Dino. "Specijalne funkcije." Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2016. https://urn.nsk.hr/urn:nbn:hr:126:313983

Škrobar, Dino. "Specijalne funkcije." Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2016. https://urn.nsk.hr/urn:nbn:hr:126:313983

Škrobar, D. (2016). 'Specijalne funkcije', Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, accessed 19 October 2019, https://urn.nsk.hr/urn:nbn:hr:126:313983

Škrobar D. Specijalne funkcije [Master's thesis]. Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics; 2016 [cited 2019 October 19] Available at: https://urn.nsk.hr/urn:nbn:hr:126:313983

D. Škrobar, "Specijalne funkcije", Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, Osijek, 2016. Available at: https://urn.nsk.hr/urn:nbn:hr:126:313983

Metadata
TitleSpecijalne funkcije
Title (english)Special functions
AuthorDino Škrobar
MentorMihaela Ribičić Penava (mentor)
GranterJosip Juraj Strossmayer University of Osijek
Department of Mathematics
(Chair of Pure Mathematics)
(Algebra and Calculus Research Group)
Osijek
Defense date and country2016-08, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Mathematical Analysis
Abstract
Specijalne funkcije su posebna vrsta funkcija u matematici koje su otkrivene ili definirane prilikom rješavanja određenih problema u matematici i fizici. Općenito ih dijelimo prema tome kako su definirane: u obliku određenih integrala ili u obliku beskonačnih konvergentnih redova. U ovom diplomskom radu proučavane su sljedeće specijalne funkcije: gama i beta funkcija koje u obje definirane kao određeni integrali te Riemannova zeta funkcija, hipergeometrijske funkcije i Besselove funkcije koje su definirane kao redovi. Osim definicije, za svaku su specijalnu funkciju navedeni najbitniji rezultati kao što su karakteristične funkcijske jednadžbe, najvažnija svojstva te su iskazane veze s drugim specijalnim, ali i elementarnim funkcijama. Završni dio diplomskog rada bavi se primjenama proučavanih specijalnih funkcija. Prikazana je uporaba gama i beta funkcije u računanju točnih vrijednosti određenih integrala te u teoriji vjerojatnosti. Besselove funkcije pokazuju se važnima u fizici jer se pojavljuju kao rješenja diferencijalnih jednadžbi kojima se modeliraju brojne pojave u prirodi. Riemannova zeta funkcija koristi se najviše u teoriji brojeva, a posebno je bitna u dokazu tvrdnje da postoji beskonačno mnogo prostih brojeva.
Abstract (english)
Special functions are special type of functions in mathematics, discovered or defined in solving certain problems in mathematics and physics. Generally, there are two types of special functions: one defined in term of definite integrals and in a form of infinite convergent series. This paper is about five special functions: Gamma and Beta functions which are both defined as definite integrals and Riemann zeta function, Hypergeometric functions and Bessel functions which are defined as infinite convergent series. Some important properies and characteristic functional equations are given in this paper for every of defined functions. The final part of this paper gives some of the most important applications of defined functions. Gamma and Beta functions are both used in solving definite integrals and also in Probability Theory. Bessel functions are often used in Physics and Riemann zeta function in Number Theory. Riemann zeta function is very important in proof that there are infinitely many prime numbers.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:126:313983
Study programmeTitle: Mathematics; specializations in: Financial and Statistical Mathematics, Mathematics and Computer Science, Industrial and Applied Mathematics
Course: Financial and Statistical Mathematics
Study programme type: university
Study level: graduate
Academic / professional title: magistar/magistra matematike (magistar/magistra matematike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
Terms of usehttp://rightsstatements.org/vocab/InC/1.0/
Created on2016-09-08 07:09:53