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ArcTanh

ArcTanh[z]
gives the inverse hyperbolic tangent

of the complex number

MORE INFORMATION

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 .

EXAMPLES

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Basic Examples (3)

Evaluate numerically:

Series expansion about the origin:

Sum the series:

Evaluate numerically:

In[1]:=

Out[1]=

In[1]:=

Out[1]=

Series expansion about the origin:

In[1]:=

Out[1]=

Sum the series:

In[2]:=

Out[2]=

Scope (7)

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:

Generalizations & Extensions (3)

ArcTanh can be applied to power series:

ArcTanh can deal with real-valued intervals:

Infinite arguments give symbolic results:

Applications (2)

Find the rapidity corresponding to a speed of 0.999 times the speed of light:

Branch cuts of ArcTanh:

Properties & Relations (3)

Express ArcTanh using Log:

Convert back:

ArcTanh is a special case of some special functions: