# Is there a function for falling factorial in Mathematica

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

fallfact[x_,k_]:=$\prod_{j=0}^{k-1}(x-j)$

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

• FactorialPower – ciao Apr 10 '14 at 6:50
• @rasher Nice, I couldn't find it. THank you. You can write your comment as an answer and I'll check it – Remi.b Apr 10 '14 at 6:52
• Nah, would feel goofy getting points for that :-) – ciao Apr 10 '14 at 6:53
• @rasher just saw that--- lol -- erm, well, I... is this easily found in the documentation? – Mr.Wizard Apr 10 '14 at 6:55
• 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 ;-} – ciao Apr 10 '14 at 7:04

The falling factorial is implemented in Mathematica as FactorialPower[x, n].
$$(x)_n^{(h)}=x(x-h)\cdots(x-(n-1)h)$$
and is implemented in Mathematica as FactorialPower[x, n, h].
Documentation: FactorialPower