论文标题
贝塞尔功能的联合渐近扩展
Joint asymptotic expansions for Bessel functions
论文作者
论文摘要
我们研究了贝塞尔功能的渐近学的经典问题$j_ν（z）$和$y_ν（z）$作为参数$ z $和订单$ z $ν$进近无限。我们使用爆破分析来找到贝塞尔函数模量和相位的渐近学；这种方法会产生多均匀的共同关节渐近膨胀，在任何制度中有效。结果，我们的渐近学可以按学期划分有关参数或秩序，从而使我们可以轻松地为贝塞尔函数衍生物产生扩展。我们还讨论了光谱理论的应用，尤其是对磁盘的Dirichlet特征值的研究。
We study the classical problem of finding asymptotics for the Bessel functions $J_ν(z)$ and $Y_ν(z)$ as the argument $z$ and the order $ν$ approach infinity. We use blow-up analysis to find asymptotics for the modulus and phase of the Bessel functions; this approach produces polyhomogeneous conormal joint asymptotic expansions, valid in any regime. As a consequence, our asymptotics may be differentiated term by term with respect to either argument or order, allowing us to easily produce expansions for Bessel function derivatives. We also discuss applications to spectral theory, in particular the study of the Dirichlet eigenvalues of a disk.
