Large Degree Asymptotics of Generalized Bessel Polynomials

Details Large Degree Asymptotics of Generalized Bessel Polynomials Large Degree Asymptotics of Generalized Bessel Polynomials

2011-01-25

arxiv.org/abs/1101.4894v1

Journal of Mathematical Analysis and Applications, Vol. 377, issue 1, 2011, 30-42

Mathematics

Classical Analysis and ODEs

22 pages, 1 figure

Scientific paper

10.1016/j.jmaa.2010.10.030

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.

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