@**techreport**{RISC6579,author = {Diego Dominici},

title = {{Comparative asymptotics for discrete semiclassical orthogonal polynomials}},

language = {english},

abstract = {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.},

number = {22-11},

year = {2022},

month = {August},

keywords = {Orthogonal polynomials, asymptotic analysis },

length = {53},

license = {CC BY 4.0 International},

type = {RISC Report Series},

institution = {Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz},

address = {Altenberger Straße 69, 4040 Linz, Austria},

issn = {2791-4267 (online)}

}