Evaluate numerically:

Evaluate to high precision:

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

Evaluate for complex arguments:

Evaluate ArcSec 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 ArcSec function using MatrixFunction:

Values of ArcSec at fixed points:

Simple exact values are generated automatically:

Values at infinity:

Zero of ArcSec:

Find the value of satisfying equation :

Substitute in the value:

Visualize the result:

Plot the ArcSec function:

Plot the real part of :

Plot the imaginary part of :

Polar plot with :

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

Complex domain:

ArcSec lies between and :

Function range for arguments from the complex domain:

ArcSec is not an analytic function:

Nor is it meromorphic:

ArcSec is monotonic in a specific range:

ArcSec is injective:

ArcSec is not surjective:

ArcSec is non-negative on its real domain:

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

ArcSec is neither convex nor concave:

TraditionalForm formatting:

First derivative:

Higher derivatives:

Formula for the derivative:

Indefinite integral of ArcSec:

Definite integral over the interval :

More integrals:

Find the Taylor expansion using Series:

Plot the first three approximations for ArcSec around :

Find series expansions at branch points and branch cuts:

ArcSec can be applied to power series:

Simplify expressions involving ArcSec:

Use TrigToExp to express in terms of logarithm:

Use ExpToTrig to convert back:

Expand assuming real variables and :

Represent using ArcCos:

Representation through inverse Jacobi functions:

Represent using Hypergeometric2F1:

ArcSec can be represented in terms of MeijerG:

ArcSec can be represented as a DifferentialRoot: