Large Degree Asymptotics of Generalized Bessel Polynomials

Asymptotic expansions are given for large values of $n$ of the generalized Bessel polynomials $Y_n^μ(z)$. The analysis is based on integrals that follow from the generating functions of the polynomials. A new simple expansion is given that is valid outside a compact neighborhood of the origin in the $z-$plane. New forms of expansions in terms of elementary functions valid in sectors not containing the turning points $z=\pm i/n$ are derived, and a new expansion in terms of modified Bessel functions is given. Earlier asymptotic expansions of the generalized Bessel polynomials by Wong and Zhang (1997) and Dunster (2001) are discussed.

No reviews yet.

No comments yet.