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 average-case statistical intervals using Around:

Compute the elementwise values of an array:

Or compute the matrix Hyperfactorial function using MatrixFunction:

Values at fixed points:

Value at zero:

Hyperfactorial gives exact values for integer multiples of 1/2 and 1/4:

Find the positive minimum:

Plot the Hyperfactorial function:

Plot the real part of :

Plot the imaginary part of :

Real domain of Hyperfactorial:

Complex domain:

Function range of Hyperfactorial on the contiguous portion of its domain:

Hyperfactorial threads elementwise over lists:

Hyperfactorial is not an analytic function:

Nor is it meromorphic:

Hyperfactorial is neither non-increasing nor non-decreasing:

Hyperfactorial is not injective:

Hyperfactorial is not surjective:

Hyperfactorial is neither non-negative nor non-positive:

Hyperfactorial has both singularities and discontinuities for x≤-1:

Hyperfactorial is neither convex nor concave:

TraditionalForm formatting:

First derivative with respect to n:

Higher derivatives with respect to n:

Plot the higher derivatives with respect to n:

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: