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Large degree asymptotics of generalized Bessel polynomials. (English) Zbl 1213.33011
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 R. Wong and J.-M. Zhang [J. Comput. Appl. Math. 85, No. 1, 87–112 (1997; Zbl 0880.41027)] and T. M. Dunster [SIAM J. Math. Anal. 32, No. 5, 987–1013 (2001; Zbl 0983.33005)].
##### MSC:
 33C10 Bessel and Airy functions, cylinder functions, ${}_{0}{F}_{1}$ 33C45 Orthogonal polynomials and functions of hypergeometric type
##### References:
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