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ArcTanh

ArcTanh[z]
gives the inverse hyperbolic tangent of the complex number .
  • Mathematical function, suitable for both symbolic and numerical manipulation.
  • For certain special arguments, ArcTanh automatically evaluates to exact values.
  • ArcTanh can be evaluated to arbitrary numerical precision.
  • ArcTanh automatically threads over lists.
  • ArcTanh[z] has branch cut discontinuities in the complex plane running from to and to .
Evaluate numerically:
Series expansion about the origin:
Sum the series:
Evaluate numerically:
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Series expansion about the origin:
In[1]:=
Click for copyable input
Out[1]=
Sum the series:
In[2]:=
Click for copyable input
Out[2]=
Evaluate for complex arguments:
Evaluate to high precision:
The precision of the output tracks the precision of the input:
ArcTanh threads element-wise over lists:
Simple exact values are generated automatically:
Parity transformations are automatically applied:
TraditionalForm formatting:
ArcTanh can be applied to power series:
ArcTanh can deal with real-valued intervals:
Infinite arguments give symbolic results:
Find the rapidity corresponding to a speed of 0.999 times the speed of light:
Branch cuts of ArcTanh:
Express ArcTanh using Log:
Convert back:
ArcTanh is a special case of some special functions:
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