specfunc-clausen.texi

来自「This library is distributed in the hope 」· TEXI 代码 · 共 29 行

@cindex Clausen functions

The Clausen function is defined by the following integral,
@tex
\beforedisplay
$$
Cl_2(x) = - \int_0^x dt \log(2 \sin(t/2))
$$
\afterdisplay
@end tex
@ifinfo

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

@end ifinfo
@noindent
It is related to the dilogarithm by 
@c{$Cl_2(\theta) = \Im(Li_2(e^{i\theta}))$}
@math{Cl_2(\theta) = \Im Li_2(\exp(i\theta))}.  
The Clausen functions are declared in the header file
@file{gsl_sf_clausen.h}.

@deftypefun double gsl_sf_clausen (double @var{x})
@deftypefunx int gsl_sf_clausen_e (double @var{x}, gsl_sf_result * @var{result})
These routines compute the Clausen integral @math{Cl_2(x)}.
@end deftypefun