# Falling Factorial Notation

If $(x)_{n}$ refers to

$$x(x-1)\cdots(x-n+1)$$

then what does $(xy;x)_{n}$ refer to?

Is it

$$xy(xy-1)\ldots(xy-n+1)?$$

Thanks.

The notation in question is used on page two of this paper.

• I'm not aware of any standard usage. Where did you find it? – Christopher Carl Heckman Apr 25 '16 at 7:20
• I have added a link to the paper I found it in. – badatmath Apr 25 '16 at 7:22
• It looks like a q-Pochhammer symbol: en.wikipedia.org/wiki/Q-Pochhammer_symbol – Christopher Carl Heckman Apr 25 '16 at 7:30
• @Benedict I find your comment pretty rude. Even if it's just for curiosity, the question is certainly worth asking. – Daniel Robert-Nicoud Apr 25 '16 at 11:03
• @Benedict The thing that really bothers me about what you write is that, while you assert that your time is worth too much to spend it answering a passing curiosity, you still throw it away commenting. I can accept the fact that you don't want to take the time to write down an answer, but at least don't be so inconsistent and avoid writing anything entirely. – Daniel Robert-Nicoud Apr 25 '16 at 14:37