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of 23
pro vyhledávání: '"Šabanac, Zenan"'
In this paper, we generalise an interesting geometry problem from the 1995 edition of the International Mathematical Olympiad (IMO) using analytic geometry tools.
Comment: 9 pages, 5 figures
Comment: 9 pages, 5 figures
Externí odkaz:
http://arxiv.org/abs/2408.01071
In this paper we derive some new identities involving the Fibonacci and Lucas polynomials and the Chebyshev polynomials of the first and the second kind. Our starting point is a finite trigonometric sum which equals the resolvent kernel on the discre
Externí odkaz:
http://arxiv.org/abs/2403.12516
In this paper, we study discrete Bessel functions which are solutions to the discretization of Bessel differential equations when the forward and the backward difference replace the time derivative. We focus on the discrete Bessel equations with the
Externí odkaz:
http://arxiv.org/abs/2306.14656
We study the theta function and the Hurwitz-type zeta function associated to the Lucas sequence $U=\{U_n(P,Q)\}_{n\geq 0}$ of the first kind determined by the real numbers $P,Q$ under certain natural assumptions on $P$ and $Q$. We deduce an asymptoti
Externí odkaz:
http://arxiv.org/abs/2209.03023
Autor:
Šabanac, Zenan, Šćeta, Lamija
We derive closed formula for the heat kernel $K_\mathbb{H}$ associated to Maass-Laplacian operator $D_k$ for any real $k$ and prove that heat kernel $K_\mathbb{H}$ is strictly monotone decreasing function. We also derive some important asymptotic for
Externí odkaz:
http://arxiv.org/abs/2003.02006
Akademický článek
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Autor:
Avdispahić, Muharem, Šabanac, Zenan
A trigonometric series strongly bounded at two points and with coefficients forming a log-quasidecreasing sequence is necessarily the Fourier series of a function belonging to all $L^{p}$ spaces, $1\leq p < \infty$. We obtain new results on strong co
Externí odkaz:
http://arxiv.org/abs/1612.06250
Autor:
Avdispahić, Muharem, Šabanac, Zenan
By observing the equivalence of assertions on determining the jump of a function by its differentiated or integrated Fourier series, we generalize a previous result of Kvernadze, Hagstrom and Shapiro to the whole class of functions of harmonic bounde
Externí odkaz:
http://arxiv.org/abs/1604.05862
Autor:
Avdispahić, Muharem1 (AUTHOR), Šabanac, Zenan1 (AUTHOR) zsabanac@pmf.unsa.ba
Publikováno v:
Bulletin of the Malaysian Mathematical Sciences Society. Jul2020, Vol. 43 Issue 4, p3019-3026. 8p.
Publikováno v:
The Fibonacci Quarterly; December 2022, Vol. 60 Issue: 5 p344-354, 11p