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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 {\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)].

33C10Bessel and Airy functions, cylinder functions, ${}_0F_1$
33C45Orthogonal polynomials and functions of hypergeometric type
Full Text: DOI arXiv
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[13] Wong, R.; Zhang, J. -M.: Asymptotic expansions of the generalized Bessel polynomials, J. comput. Appl. math. 85, No. 1, 87-112 (1997) · Zbl 0880.41027 · doi:10.1016/S0377-0427(97)00131-3