Evaluate numerically:

Evaluate to high precision:

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

Evaluate for complex arguments:

Evaluate ArcSech 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 ArcSech function using MatrixFunction:

Values of ArcSech at fixed points:

Values at infinity:

Zero of ArcSech:

Find the value of satisfying equation :

Substitute in the value:

Visualize the result:

Plot the ArcSech function:

Plot the real part of :

Plot the imaginary part of :

Polar plot with :

ArcSech is defined for all real values from the interval :

Complex domain:

ArcSech achieves all real values greater than or equal to 0:

Function range for arguments from the complex domain:

ArcSech is not an analytic function:

Nor is it meromorphic:

ArcSech is decreasing over its real domain:

ArcSech is injective:

ArcSech is not surjective:

ArcSech is non-negative over its real domain:

It has both singularity and discontinuity in (-∞,0] and [1,∞):

ArcSech is neither convex nor concave:

TraditionalForm formatting:

First derivative:

Higher derivatives:

Formula for the derivative:

Indefinite integral of ArcSech:

Definite integral of ArcSech over its real domain:

More integrals:

Find the Taylor expansion using Series:

Plot the first three approximations for ArcSech around :

Find series expansions at branch points and branch cuts:

Apply ArcSech to a power series:

Simplify expressions involving ArcSech:

Use TrigToExp to express in terms of logarithm:

Convert back:

Expand assuming real variables and :

Represent using ArcCosh:

Representation through inverse Jacobi functions:

Represent using Hypergeometric2F1:

ArcSech can be represented in terms of MeijerG:

ArcSech can be represented as a DifferentialRoot: