Evaluate numerically:

Evaluate to high precision:

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

Evaluate for complex arguments:

Evaluate ArcSinh efficiently at high precision:

ArcSinh can deal with real-valued intervals:

ArcSinh threads elementwise over lists and matrices:

ArcSinh can be used with CenteredInterval objects:

Values of ArcSinh at fixed points:

Values at infinity:

Zero of ArcSinh:

Find the value of satisfying equation :

Substitute in the value:

Visualize the result:

Plot the ArcSinh function:

Plot the real part of :

Plot the imaginary part of :

Polar plot with :

ArcSinh is defined for all real and complex values:

ArcSinh achieves all real values:

Function range for arguments from the complex domain:

ArcSinh is an odd function:

ArcSinh has the mirror property :

is an analytic function of over the reals:

It is neither analytic nor meromorphic over the complexes:

ArcSinh is non-decreasing:

ArcSinh is injective:

ArcSinh is surjective:

ArcSinh is neither non-negative nor non-positive:

ArcSinh has no singularities or discontinuities:

ArcSinh is neither convex nor concave:

TraditionalForm formatting:

First derivative:

Higher derivatives:

Formula for the derivative:

Indefinite integral of ArcSinh:

Definite integral of ArcSinh over an interval centered at the origin is 0:

More integrals:

Find the Taylor expansion using Series:

Plot the first three approximations for ArcSinh around :

General term in the series expansion of ArcSinh:

Find series expansions at branch points and branch cuts:

ArcSinh can be applied to a power series:

Compute the Fourier transform using FourierTransform:

HankelTransform:

Simplify expressions involving ArcSinh:

Use TrigToExp to express ArcSinh using logarithm:

Expand assuming real variables and :

Represent using ArcCsch:

Representation through inverse Jacobi functions:

Represent using Hypergeometric2F1:

ArcSinh can be represented in terms of MeijerG:

ArcSinh can be represented as a DifferentialRoot: