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
\(\operatorname{Cl_2}(x)\).