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.

中文翻译：

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归一化贝塞尔函数的星状半径的渐近展开式

摘要 考虑了两类归一化贝塞尔函数的类星半径的大阶渐近行为。我们推导出星状半径的完全渐近展开式，并提供这些展开式系数的递推关系。证明依赖于瑞利和和渐近反演的概念。论文中采用的技术可用于处理涉及渐近展开反演的类似问题。