If I had to construct a function for falling factorial in mathematica I'd do something like that (hope I'm not mistaken):


But is there a built-in function for falling factorial in Mathematica?

  • 2
    $\begingroup$ FactorialPower $\endgroup$
    – ciao
    Apr 10, 2014 at 6:50
  • $\begingroup$ @rasher Nice, I couldn't find it. THank you. You can write your comment as an answer and I'll check it $\endgroup$
    – Remi.b
    Apr 10, 2014 at 6:52
  • 1
    $\begingroup$ Nah, would feel goofy getting points for that :-) $\endgroup$
    – ciao
    Apr 10, 2014 at 6:53
  • $\begingroup$ @rasher just saw that--- lol -- erm, well, I... is this easily found in the documentation? $\endgroup$
    – Mr.Wizard
    Apr 10, 2014 at 6:55
  • 1
    $\begingroup$ Nah, I say leave it, it is rather obscure outside of most fields. Might be a good community wiki (other names and conventions, e.g. the Pochhammer in MM is very different from the use in other fields of mathematics). Besides, I can wince as your answer gets 30 upvotes ;-} $\endgroup$
    – ciao
    Apr 10, 2014 at 7:04

1 Answer 1


According to MathWorld (a great resource with frequent references to Mathematica functions):

The falling factorial is implemented in Mathematica as FactorialPower[x, n].

A generalized version of the falling factorial can defined by


and is implemented in Mathematica as FactorialPower[x, n, h].

Documentation: FactorialPower


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