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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?

J. M.'s missing motivation
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    FactorialPower – ciao Apr 10 '14 at 06:50
  • @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 06:52
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    Nah, would feel goofy getting points for that :-) – ciao Apr 10 '14 at 06:53
  • @rasher just saw that--- lol -- erm, well, I... is this easily found in the documentation? – Mr.Wizard Apr 10 '14 at 06:55
  • 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 06:56
  • @Mr.Wizard: As "easily" found as anything there, I suppose. I don't recall it being called that anywhere in the docs, I only know it because it's widely known in combinatorics. Would be nice if V10 had a "other names" section of docs... – ciao Apr 10 '14 at 06:58
  • Interestingly if I search for "falling factorial" in the Mathematica help browser the first link is to the FactorialPower page, but "falling" doesn't seem to appear anywhere within that page. I'm torn between closing this as "easily found in the documentation" and leaving it as a signpost. What do you both think? ( @rasher ) – Mr.Wizard Apr 10 '14 at 06:59
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    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 07:04
  • This is closely related: The best method of constructing a product of consecutive terms or just a duplicate. – Artes Apr 10 '14 at 11:07

1 Answers1

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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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