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Function Repository Resource:

ClausenCl

Source Notebook

Compute the Clausen functions

Contributed by: Enrique Zeleny

ResourceFunction["ClausenCl"][n,x]

are the Clausen functions Cln(x).

Details and Options

The Clausen functions are defined in terms of polylogarithm functions.

Examples

Basic Examples

Some special values:

In[1]:=
ResourceFunction["ClausenCl"][2, \[Pi]/2]
Out[1]=
In[2]:=
FunctionExpand[ResourceFunction["ClausenCl"][2, z], 0 < x < 2 \[Pi]]
Out[2]=
In[3]:=
Sum[Cos[k x]/k^3, {k, \[Infinity]}] == ResourceFunction["ClausenCl"][3, x]
Out[3]=

Plots of Clausen functions:

In[4]:=
Plot[{ResourceFunction["ClausenCl"][1, \[Rho]], ResourceFunction["ClausenCl"][2, \[Rho]], ResourceFunction["ClausenCl"][3, \[Rho]]}, {\[Rho], 0, 2 \[Pi]}]
Out[4]=
In[5]:=
ContourPlot[
 Abs[ResourceFunction["ClausenCl"][2, x + I y]], {x, -1.5, 1.5}, {y, -1.7, 1.7}, PlotPoints -> 15, ColorFunction -> "DarkRainbow", ContourStyle -> None, Contours -> 20,
  MeshFunctions -> (#3 &), Mesh -> 20]
Out[5]=
In[6]:=
Plot3D[Im[ResourceFunction["ClausenCl"][1, x + I y]], {x, -1.5`, 1.5`}, {y, -1.7`, 1.7`}, ImageSize -> 450, PlotPoints -> 30, ColorFunction -> "DarkRainbow", MeshFunctions -> (#3 &), Mesh -> 20, PlotStyle -> Opacity[0.7`]]
Out[6]=

Requirements

Wolfram Language 11.3 (March 2018) or above

Resource History

License Information