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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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    $\begingroup$ FactorialPower $\endgroup$ – ciao Apr 10 '14 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 '14 at 6:52
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    $\begingroup$ Nah, would feel goofy getting points for that :-) $\endgroup$ – ciao Apr 10 '14 at 6:53
  • $\begingroup$ @rasher just saw that--- lol -- erm, well, I... is this easily found in the documentation? $\endgroup$ – Mr.Wizard Apr 10 '14 at 6:55
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    $\begingroup$ 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 '14 at 7:04
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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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