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undergraduate thesis
Hermiteovi polinomi
Osijek: Josip Juraj Strossmayer University of Osijek, School of Applied Mathematics and Informatics, 2024. urn:nbn:hr:126:259320
Prpić, Vanesa
Josip Juraj Strossmayer University of Osijek
School of Applied Mathematics and Informatics

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Prpić, V. (2024). Hermiteovi polinomi (Undergraduate thesis). Osijek: Josip Juraj Strossmayer University of Osijek, School of Applied Mathematics and Informatics. Retrieved from https://urn.nsk.hr/urn:nbn:hr:126:259320

Prpić, Vanesa. "Hermiteovi polinomi." Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, School of Applied Mathematics and Informatics, 2024. https://urn.nsk.hr/urn:nbn:hr:126:259320

Prpić, Vanesa. "Hermiteovi polinomi." Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, School of Applied Mathematics and Informatics, 2024. https://urn.nsk.hr/urn:nbn:hr:126:259320

Prpić, V. (2024). 'Hermiteovi polinomi', Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, School of Applied Mathematics and Informatics, accessed 19 November 2024, https://urn.nsk.hr/urn:nbn:hr:126:259320

Prpić V. Hermiteovi polinomi [Undergraduate thesis]. Osijek: Josip Juraj Strossmayer University of Osijek, School of Applied Mathematics and Informatics; 2024 [cited 2024 November 19] Available at: https://urn.nsk.hr/urn:nbn:hr:126:259320

V. Prpić, "Hermiteovi polinomi", Undergraduate thesis, Josip Juraj Strossmayer University of Osijek, School of Applied Mathematics and Informatics, Osijek, 2024. Available at: https://urn.nsk.hr/urn:nbn:hr:126:259320

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Metadata
TitleHermiteovi polinomi
Title (english)Hermite Polynomials
AuthorVanesa Prpić
MentorMihaela Ribičić Penava (mentor)
GranterJosip Juraj Strossmayer University of Osijek
School of Applied Mathematics and Informatics
Osijek
Defense date and country2024-09-20, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Mathematical Analysis
Abstract
U ovom radu ćemo definirati Hermiteove polinome i navesti njihova osnovna svojstva. Pokazat ćemo kako se mogu izraziti pomoću funkcija izvodnica te kako predstavljaju rješenje homogene linearne diferencijalne jednadžbe drugog reda. Izvest ćemo rekurzivne relacije koje oni zadovoljavaju i dokazati njihovu ortogonalnost. Zatim ćemo predstaviti Hermiteove funkcije i integralnu reprezentaciju Hermiteovih polinoma. Na kraju ćemo razmotriti Hermiteove polinome s jednim parametrom te prikazati njihove primjene u matematičkoj fizici, posebno u kvantnoj mehanici, i numeričkoj matematici.
Abstract (english)
In this paper, we will define Hermite polynomials and state their basic properties. We will show how they can be expressed using derivative functions and how they represent the solution of a homogeneous linear differential equation of the second order. We will derive recursive relations that they satisfy and prove their orthogonality. Next, we will present Hermite functions and the integral representation of Hermite polynomials. Finally, we will consider Hermite polynomials with one parameter and show their applications in mathematical physics, especially in quantum mechanics, and numerical mathematics
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:126:259320
Study programmeTitle: University Bachelor of Mathematics (univ. bacc. math.)
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
RepositoryRepository of School of Applied Mathematics and Informatics
Created on2024-10-01 07:09:29