The W_t Transcendental Function and Quantum Mechanical Applications

TL;DR

This paper explores the properties and applications of the W_t transcendental function, including its analytic structure, series expansions, and numerical evaluation methods relevant to quantum mechanics and field theory.

Contribution

It introduces the W_t function, analyzes its properties, and develops techniques for its series expansion and numerical computation in complex analysis.

Findings

Derived series expansions for small and large x

Analyzed the function's analytic structure

Developed numerical evaluation techniques

Abstract

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.