Evaluation of a ln tan integral arising in quantum field theory

TL;DR

This paper analytically evaluates a specific dilogarithmic integral relevant to hyperbolic geometry and derives new representations and relations involving special functions like the Clausen function and Catalan constant.

Contribution

It provides new analytical expressions for a dilogarithmic integral, new representations of the Clausen function and Catalan constant, and establishes novel relations between sine and Clausen function values.

Findings

New representations of the Clausen function Cl_2

Analytical evaluation of a dilogarithmic integral

New relations between sine and Clausen function values

Abstract

We analytically evaluate a dilogarithmic integral that is prototypical of volumes of ideal tetrahedra in hyperbolic geometry. We additionally obtain new representations of the Clausen function Cl_2 and the Catalan constant G=Cl_2(\pi/2), as well as new relations between sine and Clausen function values.