Asymptotic expansions of the generalized Bessel polynomials

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.