Clausen function

Summary

The Clausen function $\operatorname{Cl}_2$ is the real function $\theta \mapsto -\int_0^\theta \log \abs{2 \sin(t/2)} \, dt$, equal to the Fourier series $\sum_{k \ge 1} \sin(k\theta) / k^2$. It is the imaginary part of the dilogarithm on the unit circle. It appears in evaluations of log-sine integrals, in values such as Catalan's constant, and in volumes of hyperbolic polyhedra.