Evaluate numerically:

Evaluate to high precision:

The precision of the output tracks the precision of the input:

Evaluate for complex arguments:

Evaluate ArcCoth efficiently at high precision:

Compute worst-case guaranteed intervals using Interval and CenteredInterval objects:

Or compute average-case statistical intervals using Around:

Compute the elementwise values of an array:

Or compute the matrix ArcCoth function using MatrixFunction:

Values of ArcCoth at fixed points:

Values at infinity:

Singular points of ArcCoth:

Find the value of satisfying equation :

Simple exact values are generated automatically:

Plot the ArcCoth function:

Plot the real part of :

Plot the imaginary part of :

Polar plot with :

ArcCoth is defined for all real values except from the interval :

Complex domain:

ArcCoth achieves all real values except 0:

Function range for arguments from the complex domain:

ArcCoth is an odd function:

ArcCoth is not an analytic function:

Nor is it meromorphic:

ArcCoth is neither non-decreasing nor non-increasing:

ArcCoth is injective:

ArcCoth is not surjective:

ArcCoth is neither non-negative nor non-positive:

It has both singularity and discontinuity in [-1,1]:

ArcCoth is neither convex nor concave:

TraditionalForm formatting:

First derivative:

Higher derivatives:

Formula for the derivative:

Indefinite integral of ArcCoth:

A definite integral involving ArcCoth:

More integrals:

Find the Taylor expansion using Series:

Plot the first three approximations for ArcCoth around :

General term in the series expansion of ArcCoth:

Find series expansions at branch points and branch cuts:

ArcCoth can be applied to power series:

Simplify expressions involving ArcCoth:

Express ArcCoth using Log:

Convert back:

Expand assuming real variables and :

Represent using ArcCoth:

Representation through inverse Jacobi functions:

ArcCoth is a special case of Hypergeometric2F1:

ArcCoth can be represented in terms of MeijerG:

ArcCoth can be represented as a DifferentialRoot: