标题： W_t超越函数与量子力学应用 显示英文标题

标题： The W_t Transcendental Function and Quantum Mechanical Applications

摘要： 我们讨论了通过隐式方程 \( \mathrm\{wt\}(x)\tan[\mathrm\{wt\}(x)]=x \) 定义的函数 \( \mathrm\{wt\}(x) \)，该函数出现在某些量子力学和场论应用中。 我们研究了它的解析结构，为小 \( x \) 和大 \( x \) 分别发展了级数展开，并提供了在复平面上对其进行数值评估的各种方法。 显示英文摘要

摘要： We discuss the function wt(x) defined via the implicit equation wt(x)*tan[wt(x)]=x which appears in certain quantum mechanical and field theoretic applications. We investigate its analytic structure, develop series expansions for both small and large x, and provide various techniques for its numerical evaluation in the complex plane.