Large Degree Asymptotics of Generalized Bessel Polynomials

Abstract

Asymptotic expansions are given for large values of $n$ of the generalized Bessel polynomials $Y_n^{\mu }(z)$. The analysis is based on integrals that follow from the generating functions of the polynomials. A new simple expansion is given that is valid outside a compact neighborhood of the origin in the $z-$plane. New forms of expansions in terms of elementary functions valid in sectors not containing the turning points $z=\pm i/n$ are derived, and a new expansion in terms of modified Bessel functions is given. Earlier asymptotic expansions of the generalized Bessel polynomials by Wong and Zhang (1997) and Dunster (2001) are discussed.

22 pages, 1 figure

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