6 papers
Resultants, Recursive Formulas and Binet Formulas for Verlinde Sums
Jay Jorgenson, Anders Karlsson, Lejla Smajlović
We study Verlinde sums , which for our purposes are finite sums of trigonometric functions , associated to . In this article we prove the fo…
Evaluating Verlinde sums using spectral graph theory
Jay Jorgenson, Anders Karlsson, Lejla Smajlović
We realize the Verlinde sums , up to an explicit factor, as the values at of the spectral zeta function of a higher-order Laplace operator on the trian…
Constructing heat kernels on infinite graphs
Jay Jorgenson, Anders Karlsson, Lejla Smajlović
Let be an infinite, edge- and vertex-weighted graph with certain reasonable restrictions. We construct the heat kernel of the associated Laplacian using an adaptation of the pa…
Relations between Chebyshev, Fibonacci and Lucas polynomials via trigonometric sums
Lejla Smajlović, Zenan Šabanac, Lamija Šćeta
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 fi…
The parametrix construction of the heat kernel on a graph
Gautam Chinta, Jay Jorgenson, Anders Karlsson +1
In this paper we develop the parametrix approach for constructing the heat kernel on a graph . In particular, we highlight two specific cases. First, we consider the case when $…
Discrete Bessel functions and discrete wave equation
Amar Bašić, Lejla Smajlović, Zenan Šabanac
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 th…