The Clausen function is defined by the following integral,

     Cl_2(x) = - \int_0^x dt \log(2 \sin(t/2))

It is related to the dilogarithm by $Cl_2(\theta) = \Im(Li_2(e^i\theta))$ Cl_2(\theta) = \Im Li_2(\exp(i\theta)). The Clausen functions are declared in the header file gsl_sf_clausen.h.

 -- Function: double gsl_sf_clausen (double X)
 -- Function: int gsl_sf_clausen_e (double X, gsl_sf_result * RESULT)
     These routines compute the Clausen integral Cl_2(x).