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Uniform asymptotic approximation and numerical evaluation of the reverse generalized Bessel polynomial zeros

Abstract: Uniform asymptotic expansions are derived for the zeros of the reverse generalized Bessel polynomials of large degree $n$ and real parameter $a$. It is assumed that $-\Delta_{1} n+\frac{3}{2} \leq a \leq \Delta_{2} n$ for fixed arbitrary $\Delta_{1} \in (0,1)$ and bounded positive $\Delta_{2}$. For this parameter range, at most one of the zeros is real, with the rest being complex conjugates. The new expansions are uniformly valid for all the zeros and are shown to be highly accurate for moderate or large values of $n$. They are consequently used as initial values in a very efficient numerical algorithm designed to obtain the remaining complex zeros using a Taylor series.

 Fuente: Electronic Transactions on Numerical Analysis, 2026, 65, 140-155

 Publisher: Kent State University

 Year of publication: 2026

 No. of pages: 16

 Publication type: Article

 DOI: 10.1553/etna_vol65s140

 ISSN: 1068-9613,1097-4067

 Spanish project: PID2021-127252NB-I00

 Publication Url: https://epub.oeaw.ac.at/?arp=0x0041919f