This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.
View current documentation (Version 11.1)


gives the double factorial of n.
  • Mathematical function, suitable for both symbolic and numerical manipulation.
  • .
  • n!! is a product of even numbers for n even, and odd numbers for n odd.
  • Factorial2 can be evaluated to arbitrary numerical precision.
Integer values:
Evaluate numerically:
Integer values:
Click for copyable input
Click for copyable input
Evaluate numerically:
Click for copyable input
Evaluate for large arguments:
Evaluate at negative integers:
Plot double factorial:
Evaluate for complex arguments:
Factorial2 threads element-wise over lists:
Infinite arguments give symbolic results:
Series expansion at poles:
Series expansion at infinity (generalized Stirling approximation):
Plot of the absolute value of Factorial2 in the complex plane:
Use FunctionExpand to expand double factorial into Gamma function:
Use FullSimplify to simplify expressions involving double factorials:
Sums involving Factorial2:
Generating function:
Recover the original power series:
Products involving double factorial:
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 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:
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