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master's thesis
Hipergeometrijske funkcije
2021. urn:nbn:hr:126:886036
Bijelić, Aleksandra
Josip Juraj Strossmayer University of Osijek
Department of Mathematics
Chair of Pure Mathematics and Mathematics Teaching
Probability, Mathematical Statistics and Data Science Research Group

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Bijelić, A. (2021). Hipergeometrijske funkcije (Master's thesis). Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics. Retrieved from https://urn.nsk.hr/urn:nbn:hr:126:886036

Bijelić, Aleksandra. "Hipergeometrijske funkcije." Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2021. https://urn.nsk.hr/urn:nbn:hr:126:886036

Bijelić, Aleksandra. "Hipergeometrijske funkcije." Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2021. https://urn.nsk.hr/urn:nbn:hr:126:886036

Bijelić, A. (2021). 'Hipergeometrijske funkcije', Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, accessed 08 April 2025, https://urn.nsk.hr/urn:nbn:hr:126:886036

Bijelić A. Hipergeometrijske funkcije [Master's thesis]. Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics; 2021 [cited 2025 April 08] Available at: https://urn.nsk.hr/urn:nbn:hr:126:886036

A. Bijelić, "Hipergeometrijske funkcije", Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, Osijek, 2021. Available at: https://urn.nsk.hr/urn:nbn:hr:126:886036

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Metadata
TitleHipergeometrijske funkcije
Title (english)Hypergeometric Functions
AuthorAleksandra Bijelić
MentorDragana Jankov Maširević (mentor)
Committee memberMihaela Ribičić Penava (predsjednik povjerenstva)
Committee memberDragana Jankov Maširević (član povjerenstva)
Committee memberLjiljana Primorac Gajčić (član povjerenstva)
GranterJosip Juraj Strossmayer University of Osijek
Department of Mathematics
(Chair of Pure Mathematics and Mathematics Teaching)
(Probability, Mathematical Statistics and Data Science Research Group)
Osijek
Defense date and country2021-06-18, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Mathematical Analysis
Abstract
U ovom radu definirali smo opći oblik hipergeometrijske funkcije te se bliže upoznali s nekim specijalnim funkcijama kao što su generalizirane hipergeometrijske funkcije, Gaussova hipergeometrijska funkcija i konfluentna hipergeometrijska funkcija. Iskazali smo i dokazali konvergenciju generalizirane i Gaussove hipergeometrijske funkcije te integralnu reprezentaciju Gaussove funkcije. Pored generalizirane i Gaussove funkcije za koju vrijedi da je \(p\leqq q+1\), proučili smo i hipergeometrijsku funkciju za koju vrijedi da je p, q = 1. Takvu funkciju zovemo konfluentna hipergeometrijska funkcija. Promotrili smo diferencijalnu jednadžbu čije je jedno rješenje konfluentna funkcija te pronašli ostala rješenja. Pokazali smo da se mnoge elementarne funkcije mogu prikazati pomoću generaliziranih hipergeometrijskih funkcija. Pored funkcija s jednom varijablom, definirali smo neke hipergeometrijske funkcije s dvije varijable kao što su Appelove funkcije, Hornovi redovi, konfluentna hipergeometrijska funkcija s dvije varijable te Kampé de Fériet funkcija. Pokazali smo njihovu vezu sa generaliziranim hipergeometrijskim funkcijama te njihov međusobni odnos.
Abstract (english)
In this thesis, we define the general form of hypergeometric functions and get acquainted with some special functions such as Generalized hypergeometric functions, Gauss hypergeometric function and confluent hypergeometric function. We have stated and proved the convergence of the Generalized and Gaussian hypergeometric function and integral representation of Gaussian function. In addition to the Generalized and Gaussian function which is valid to be \(p\leqq q+1\), we also studied the hypergeometric function which is valid to be p, q = 1. This function is called confluent hypergeometric function. We observed the differential equation whose solution is confluent function and found other solutions. We have shown that many elementary functions can be represented by Generalized hypergeometric functions. In addition to functions with one variable, we defined some Hypergeometric functions with two variables, such as Apple Series, Horn Series, confluent hypergeometric functions with two variables and Kampé de Fériet. We have shown their connection with Generalized hypergeometric function and their interrelationship
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:126:886036
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 useLicence In copyright icon
Created on2021-06-23 06:57:13