This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.
View current documentation (Version 11.1)

ArcCoth

ArcCoth[z]
gives the inverse hyperbolic cotangent of the complex number .
  • Mathematical function, suitable for both symbolic and numerical manipulation.
  • For certain special arguments, ArcCoth automatically evaluates to exact values.
  • ArcCoth can be evaluated to arbitrary numerical precision.
  • ArcCoth automatically threads over lists.
  • ArcCoth[z] has a branch cut discontinuity in the complex plane running from to .
Evaluate numerically:
Series expansion:
Evaluate numerically:
In[1]:=
Click for copyable input
Out[1]=
 
In[1]:=
Click for copyable input
Out[1]=
 
Series expansion:
In[1]:=
Click for copyable input
Out[1]=
Evaluate for complex arguments:
Evaluate to high precision:
The precision of the output tracks the precision of the input:
ArcCoth threads element-wise over lists:
Simple exact values are generated automatically:
Parity transformations are automatically applied:
TraditionalForm formatting:
ArcCoth can be applied to power series:
ArcCoth can deal with real-valued intervals:
Infinite arguments give symbolic results:
Branch cuts of ArcCoth:
Express ArcCoth using Log:
Convert back:
New in 1