Talk:Chu-Vandermonde Identity/Extended

I think something is missing here.

Instead of:

$\ds \sum_{k \mathop \in \Z} \dbinom r {\alpha + k} \dbinom s {\beta - k}$

Shouldn't it be

$\ds \sum_{k \mathop \in \Z} \dbinom r {\alpha + k} \dbinom s {\beta - k} = \binom {r + s} {\alpha + \beta}$

or something like that? (Shouldn't that sum equal something?)

Also - a few other online sources have the Extended Chu-Vandermonde Identity as what is shown below:

$\ds \paren {r + s}^{\overline n} = \sum_{k \mathop = 0}^n \dbinom n k r^{\overline k} s^{\overline {n-k} }$

--Robkahn131 (talk) 02:04, 6 December 2022 (UTC)

Online sources in general are not worth the paper they are printed on, so unless they can be backed up by solid officially published citations, as far as $\mathsf{Pr} \infty \mathsf{fWiki}$ is concerned they don't exist.

If the mathematical development contributing towards such a definition can be exploited and transferred to $\mathsf{Pr} \infty \mathsf{fWiki}$, then we should be able to incorporate such development. If we then need to rename our existing pages, then that's what we do. --prime mover (talk) 06:43, 6 December 2022 (UTC)