# 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?

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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
ha ha I didn't really know where to find this documentation. I actually went on the MathWorld link you gave in your answer but didn't realize that the function name in Mathematica was written on that page. Thank you! – Remi.b Apr 10 '14 at 6:56

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

$$(x)_n^{(h)}=x(x-h)\cdots(x-(n-1)h)$$

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

Documentation: FactorialPower

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