Evaluate numerically:

Evaluate to high precision:

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

Complex number inputs:

Evaluate 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 LogBarnesG function using MatrixFunction :

Values at fixed points:

Value at infinity:

Value at zero:

Find the first positive maximum:

Plot the LogBarnesG function:

Plot the real part of TemplateBox[{z}, LogBarnesG]:

Plot the imaginary part of TemplateBox[{z}, LogBarnesG]:

Real domain of LogBarnesG :

Complex domain:

Function range of LogBarnesG :

LogBarnesG is not an analytic function of x:

LogBarnesG is neither non-increasing nor non-decreasing:

LogBarnesG is not injective:

LogBarnesG is surjective:

LogBarnesG is neither non-negative nor non-positive:

LogBarnesG has both singularities and discontinuities for negative values:

LogBarnesG is neither convex nor concave:

TraditionalForm formatting:

First derivatives with respect to z:

Higher derivatives with respect to z:

Plot the higher derivatives with respect to z:

Formula for the ^(th) derivative with respect to z:

Find the Taylor expansion using Series :

Plots of the first three approximations around :

Find the series expansion at Infinity :

Find series expansion for an arbitrary symbolic direction :

Taylor expansion at a generic point: