Asymptotic expansions for the radii of starlikeness of normalised Bessel functions

Abstract

The asymptotic behaviour, with respect to the large order, of the radii of starlikeness of two types of normalised Bessel functions is considered. We derive complete asymptotic expansions for the radii of starlikeness and provide recurrence relations for the coefficients of these expansions. The proofs rely on the notion of Rayleigh sums and asymptotic inversion. The techniques employed in the paper could be useful to treat similar problems where inversion of asymptotic expansions is involved.

arXiv comment11 pages, revised version, accepted for publication in Journal of Mathematical Analysis and Applications. The exposition was improved based on the referee's comments

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