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Zbl 1213.33011
López, José Luis; Temme, Nico M.
Large degree asymptotics of generalized Bessel polynomials.
(English)
[J] J. Math. Anal. Appl. 377, No. 1, 30-42 (2011). ISSN 0022-247X

The authors present several asymptotic expansions for generalized Bessel polynomials $Y_n^\mu$ for large degrees $n$. The expansions are carried out in terms of either Laguerre polynomials, Airy functions, or modified Bessel functions. The proofs are based on generating functions and integral representations for the $Y_n^\mu$. Some of the expansions in the paper are closely related to earlier results of {\it R. Wong} and {\it J.-M. Zhang} [J. Comput. Appl. Math. 85, No. 1, 87--112 (1997; Zbl 0880.41027)] and {\it T. M. Dunster} [SIAM J. Math. Anal. 32, No. 5, 987--1013 (2001; Zbl 0983.33005)].
[Michael Voit (Dortmund)]
MSC 2000:
*33C10 Cylinder functions, etc.
33C45 Orthogonal polynomials and functions of hypergeometric type

Keywords: Bessel polynomials; asymptotic expansions; Laguerre polynomials; modified Bessel functions; Kummer functions

Citations: Zbl 0880.41027; Zbl 0983.33005

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