Pochhammer symbol

Let $n$ be a positive integer. If we denote by (x)_n:=x(x+1)...(x+n-1)

It is known that (c-b)_n/(c)_n is expressed by the hypergeometric function 2F_1.

Now let I be a subset of {0,1,2,..,n-1} and set $(x){n,I}:=\prod{i\in I}(x+i)$.

Is there a way to express (c-b){n,I}/(c){n,I} by the hypergeometric function 2F_1 or a modified version of it ?

Thanks in advance.

flag	asked Apr 24 2011 at 13:31 mostafa 165●7

hi mostafa, did you get a chance to read the faq for this website?? – S. Sra Apr 24 2011 at 13:39

What kind of subsets are you looking at? If you allow completely random subsets, then I don't think that there's any kind of reasonable answer to your question. – André Henriques Apr 24 2011 at 17:04

Usually, people woud say that the hypergeometric function is expressed by the product, not the other way around. – thei Apr 24 2011 at 18:27

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