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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 μ 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 μ . 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:
33C10Bessel and Airy functions, cylinder functions, 0 F 1
33C45Orthogonal polynomials and functions of hypergeometric type
References:
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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