Clausen Function

The Clausen function is defined by the following integral,

\[\operatorname{Cl_2}(x) = -\int_0^x \log(2 \sin(t/2)) dt\]

It is related to the dilogarithm by

\[\operatorname{Cl_2}(\theta) = \operatorname{Im} \operatorname{Li_2}(\exp(i\theta)).\]
gsl_sf_clausen(x)

This routine computes the Clausen integral \(\operatorname{Cl_2}(x)\).