Abstract
In this paper, we investigate the asymptotic behavior of the generalized Bessel polynomials y n ( z; a). Let z = α (n + 1) . We first derive infinite asymptotic expansions for y n ( 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 y n ( 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 y n ( z; a) near α = i.
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