Evaluate at integer values:

Evaluate at real values:

Plot over a subset of the reals:

Plot over a subset of the complexes:

Series expansion at the origin:

Series expansion at Infinity:

Series expansion at a singular point:

Infinite arguments give symbolic results:

Series expansion at poles:

Series expansion at infinity (generalized Stirling approximation):

Plot of the absolute value of the double factorial in the complex plane:

An infinite series for in terms of the factorial and double factorial:

Calculate the first 30 digits of using this series:

Compare with numerically evaluating Pi:

Verify an expression for the Catalan numbers in terms of double factorials:

For an odd prime, a generalization of Wilson's theorem states that . Verify for the first few odd primes:

A determinantal representation for the odd double factorials:

Use FunctionExpand to express the double factorial in terms of the Gamma function:

Use FullSimplify to simplify expressions involving double factorials:

Sums involving Factorial2:

Generating function:

Recover the original power series:

Products involving the double factorial:

Factorial2 can be represented as a DifferenceRoot:

FindSequenceFunction can recognize the Factorial2 sequence:

The exponential generating function for Factorial2:

Large arguments can give results too large to be computed explicitly, even approximately:

Smaller values work:

Machine-number inputs can give high‐precision results:

To compute a repeated factorial, use instead of :

Plot Factorial2 at infinity:

Find the numbers of digits 0 through 9 in 10000!!:

Plot the ratio of doubled factorials over double factorial: