Year: 2023
Type: preprint
Abstract: We consider polynomials orthogonal on the unit circle with respect to the complex-valued measure $z^{ω-1}\mathrm{d} z$, where $ω\in\mathbb{R}\setminus\{0\}$. We derive their explicit form, a generating function and several recurrence relations. These polynomials possess an intriguing pattern of zeros which, as $ω$ varies, are reminiscent of a firework explosion. We prove this pattern in a rigorous manner.
Source: arXiv (Cornell University)
Authors: Cantero, María José, Iserles, Arieh
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4385825558