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Diffstat (limited to 'gsl-1.9/doc/specfunc-clausen.texi')
| -rw-r--r-- | gsl-1.9/doc/specfunc-clausen.texi | 28 |
1 files changed, 28 insertions, 0 deletions
diff --git a/gsl-1.9/doc/specfunc-clausen.texi b/gsl-1.9/doc/specfunc-clausen.texi new file mode 100644 index 0000000..b0987c2 --- /dev/null +++ b/gsl-1.9/doc/specfunc-clausen.texi @@ -0,0 +1,28 @@ +@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 |