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Asymptotic expansions of the generalized Bessel polynomials

    This research was partially supported by a RGC grant from the University Grant Committee of Hong Kong.

    https://doi.org/10.1142/9789814656054_0033Cited by:0 (Source: Crossref)
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    Abstract:

    In this paper, we investigate the asymptotic behavior of the generalized Bessel polynomials Yn(z; a). Let z = α/(n + 1). We first derive infinite asymptotic expansions for yn(z; a) when α lies in various regions of the complex plane, except when α is near ± i. Then we construct uniform asymptotic expansions for Yn(z; a) in neighborhoods of α = ± i. These expansions involve the Airy function and its derivative. Finally, we use these approximations to study the asymptotic behavior of the zeros of Yn(z; a) near α = i.