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undergraduate thesis
Horadamovi polinomi
2019. urn:nbn:hr:126:621748
Pribisalić, Iva
Josip Juraj Strossmayer University of Osijek
Department of Mathematics
Chair of Pure Mathematics and Mathematics Teaching
Algebra, Analysis and Number Theory Research Group

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Pribisalić, I. (2019). Horadamovi polinomi (Undergraduate thesis). Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics. Retrieved from https://urn.nsk.hr/urn:nbn:hr:126:621748

Pribisalić, Iva. "Horadamovi polinomi." Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2019. https://urn.nsk.hr/urn:nbn:hr:126:621748

Pribisalić, Iva. "Horadamovi polinomi." Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2019. https://urn.nsk.hr/urn:nbn:hr:126:621748

Pribisalić, I. (2019). 'Horadamovi polinomi', Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, accessed 10 November 2024, https://urn.nsk.hr/urn:nbn:hr:126:621748

Pribisalić I. Horadamovi polinomi [Undergraduate thesis]. Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics; 2019 [cited 2024 November 10] Available at: https://urn.nsk.hr/urn:nbn:hr:126:621748

I. Pribisalić, "Horadamovi polinomi", Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, Osijek, 2019. Available at: https://urn.nsk.hr/urn:nbn:hr:126:621748

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Metadata
TitleHoradamovi polinomi
Title (english)Horadam Polynomials
AuthorIva Pribisalić
MentorMihaela Ribičić Penava (mentor)
GranterJosip Juraj Strossmayer University of Osijek
Department of Mathematics
(Chair of Pure Mathematics and Mathematics Teaching)
(Algebra, Analysis and Number Theory Research Group)
Osijek
Defense date and country2019-09-25, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Mathematical Analysis
Abstract
U ovom radu upoznat ćemo se s polinomima zadanim rekurzivnim formulama. Navest ćemo nekoliko vrsta takvih polinoma te objasniti Binetovu formulu vezanu uz Fibonaccijeve polinome. Detaljnije ćemo obraditi dvije vrste polinoma, Pellove i Pell-Lucasove. Opisat ćemo njihova svojstva i grafički prikazati neke od polinoma. Osim Pell-Lucasovih, obradit ćemo i općenitiju vrstu, k-Pell-Lucasove polinome. Proučit ćemo pripadne matrične zapise te konvoluciju polinoma. Konačno, dokazat ćemo jednakosti koje povezuju Pellove i PellLucasove polinome. Navest ćemo jednakosti koje vrijede izmedu Fibonaccijevih, Pellovih i Pell-Lucasovih brojeva te opisati na koji način se oni mogu primijeniti u kombinatorici.
Abstract (english)
In this paper we will introduce type of polynomials defined by the recursive formulas. We will mention some of these polynomials and explain Binet formula. Furthermore, we will present two of the polynomials, Pell and Pell-Lucas, in detail. Some properties and graphical representation will also be shown. Besides that, k-Pell-Lucas polynomials will be mentioned. We will see some matrix techniques for these polynomials, as well as convolution. Finally, equalities that link Pell and Pell-Lucas polynomials will be proven. After that, we will mention the numbers which are obtained through certain polynomials. Some equalities will be used to prove connection between these numbers and trigonometric functions. We will end this paper with application of these numbers in Combinatorics.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:126:621748
Study programmeTitle: University undergraduate study programme in mathematics
Study programme type: university
Study level: undergraduate
Academic / professional title: sveučilišni/a prvostupnik/prvostupnica (baccalaureus/baccalaurea) matematike (sveučilišni/a prvostupnik/prvostupnica (baccalaureus/baccalaurea) matematike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2019-09-30 11:44:43