engCantero Medina, María JoséIserles, AriehOn skyburst polynomials and their zerosART-2023-148961We consider polynomials orthogonal on the unit circle with respect to the complex-valued measure z ω−1 dz, where ω ∈ R\ {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.2023http://zaguan.unizar.es/record/170468http://zaguan.unizar.es/record/170468oai:zaguan.unizar.es:170468info:eu-repo/grantAgreement/ES/DGA/E48-23Rinfo:eu-repo/grantAgreement/ES/MICINN/PID2021-124472NB-I00Dolomites Research Notes on Approximation 16, 1 (2023), 31-41by-nc-ndhttps://creativecommons.org/licenses/by-nc-nd/4.0/deed.esinfo:eu-repo/semantics/openAccess