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7.6 Clausen Functions

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(\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).