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undergraduate thesis
Gegenbauerovi polinomi
2021. urn:nbn:hr:126:327439
Ujić, Nataša
Josip Juraj Strossmayer University of Osijek
Department of Mathematics

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Ujić, N. (2021). Gegenbauerovi polinomi (Undergraduate thesis). Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics. Retrieved from https://urn.nsk.hr/urn:nbn:hr:126:327439

Ujić, Nataša. "Gegenbauerovi polinomi." Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2021. https://urn.nsk.hr/urn:nbn:hr:126:327439

Ujić, Nataša. "Gegenbauerovi polinomi." Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2021. https://urn.nsk.hr/urn:nbn:hr:126:327439

Ujić, N. (2021). 'Gegenbauerovi polinomi', Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, accessed 12 November 2024, https://urn.nsk.hr/urn:nbn:hr:126:327439

Ujić N. Gegenbauerovi polinomi [Undergraduate thesis]. Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics; 2021 [cited 2024 November 12] Available at: https://urn.nsk.hr/urn:nbn:hr:126:327439

N. Ujić, "Gegenbauerovi polinomi", Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, Osijek, 2021. Available at: https://urn.nsk.hr/urn:nbn:hr:126:327439

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Metadata
TitleGegenbauerovi polinomi
Title (english)Gegenbauer Polynomials
AuthorNataša Ujić
MentorMihaela Ribičić Penava (mentor)
GranterJosip Juraj Strossmayer University of Osijek
Department of Mathematics
Osijek
Defense date and country2021-09-24, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Mathematical Analysis
Abstract
U ovom ćemo radu definirati Gegenbauerove polinome i predstaviti neka njihova osnovna svojstva. Pokazat ćemo da se mogu zapisati pomoću funkcija izvodnica, ali i da predstavljaju rješenje homogene linearne diferencijalne jednadžbe drugog reda. Izvest ćemo izraze za neke rekurzivne relacije koje zadovoljavaju. Štoviše, pokazat ćemo da zadovoljavaju tročlanu rekurziju. U nastavku rada prikazat ćemo oblik Rodriguesove formule u slučaju Gegenbauerovih polinoma. Osim toga, ukratko ćemo navesti osnovne informacije o Jacobijevim polinomima, kao proširenju Gegenbauerovih polinoma, te povezanost s ostalim klasama ortogonalnih polinoma. Na kraju ćemo navesti neke od primjena Gegenbauerovih polinoma u području matematičke fizike, s naglaskom na entropiji, i numeričke matematike, gdje ćemo istaknuti Gaussove kvadraturne formule.
Abstract (english)
In this paper we will define Gegenbauer polynomials and present some of their basic properties. We will show that they can be written using generating functions, but also that they represent solution of homogeneous linear differential equation of the second order. We will derive some recurrence relations that they satisfy. Moreover, it will be shown that they satisfy the three-term recurrence relation. In the continuation of the paper, we will present Rodrigues’ formula in the case of Gegenbauer polynomials. Furthermore, we will briefly provide basic information about Jacobi polynomials, as generalization of Gegenbauer polynomials, and the connection with other classes of orthogonal polynomials. Finally, there will be given some of the applications of Gegenbauer polynomials in the field of mathematical physics, with emphasis on information entropy, and numerical mathematics, where Gaussian quadrature formulas will be pointed out.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:126:327439
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 on2021-10-06 06:46:26