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arXiv · 1101.4894

Large Degree Asymptotics of Generalized Bessel Polynomials

José Luis López·Nico M. Temme
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Abstract

Asymptotic expansions are given for large values of $n$ of the generalized Bessel polynomials $Y_n^μ(z)$. 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.

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José Luis López, Nico M. Temme. 2011-01-25. Large Degree Asymptotics of Generalized Bessel Polynomials. https://doi.org/10.1016/j.jmaa.2010.10.030

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