Diego Dominici,
"Comparative asymptotics for discrete semiclassical orthogonal polynomials"
, Serie RISC Report Series, Nummer 22-11, RISC, JKU, Hagenberg, Linz, 8-2022, ISSN: 2791-4267
Original Titel:
Comparative asymptotics for discrete semiclassical orthogonal polynomials
Sprache des Titels:
Englisch
Original Kurzfassung:
We study the ratio $frac{P_{n}left( x;zright) }{phi_{n}left( xright) }$ asymptotically as $nrightarrowinfty,$ where the polynomials $P_{n}left( x;zright) $ are orthogonal with respect to a discrete linear functional and $phi_{n}left( xright) $ denote the falling factorial polynomials. We give recurrences that allow the computation of high order asymptotic expansions of $P_{n}left( x;zright) $ and give examples for most discrete semiclassical polynomials of class $sleq2.$ We show several plots illustrating the accuracy of our results.
Forschungs-