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 BarnesG function using MatrixFunction:

Value at infinity:

Value at zero:

Evaluate symbolically at half‐integer arguments:

Evaluate symbolically at integer multiples of 1/4:

Find the first positive maximum:

Plot the BarnesG function:

Plot the real part of :

Plot the imaginary part of :

BarnesG is defined for all real and complex values:

Approximate function range of BarnesG:

BarnesG is an analytic function of x:

BarnesG is neither non-increasing nor non-decreasing:

BarnesG is not injective:

BarnesG is surjective:

BarnesG is neither non-negative nor non-positive:

BarnesG has no singularities or discontinuities:

BarnesG is neither convex nor concave:

TraditionalForm formatting:

First derivative with respect to z:

Higher derivatives with respect to z:

Plot the higher derivatives with respect to z:

Find the Taylor expansion using Series:

Plots of the first three approximations around :

Taylor expansion at a generic point:

Find the series expansion at Infinity: