.. index:: Clausen functions

The Clausen function is defined by the following integral,

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   .. math:: Cl_2(x) = - \int_0^x dt \log{\left( 2 \sin{(t/2)} \right)}

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

It is related to the :ref:`dilogarithm <dilog-function>` by 

:math:`Cl_2(\theta) = \Im Li_2(\exp(i\theta))`.

The Clausen functions are declared in the header file

:file:`gsl_sf_clausen.h`.

.. function:: double gsl_sf_clausen (double x)

              int gsl_sf_clausen_e (double x, gsl_sf_result * result)

   These routines compute the Clausen integral :math:`Cl_2(x)`.