Talk:Limit to Infinity of Binomial Coefficient over Power

As regards the commit comment "First proof seems to support this". Are we completely sure about this? I've never seen Stirling's Formula for Gamma Function applied to the complex plane. Stirling's Formula, on which this is based, is proven only for the real case.

In fact in general it is considered not a good idea to "just" change the statement of any proof because it "seems" better, especially if said proof statement is quoted directly from a given source as provided in the "Sources" section.

This overwhelmingly applies to unsourced amendments and additions.

If you can find a specific instance of where this result is stated for the full domain, then please cite it (and FFS not from ****ing StackExchange). Otherwise, with the best will in the world, we will inevitably end up with unsound and unreliable content.

Sorry to get heavy-handed about this, but we had a contributor who consistently (and indeed, defiantly) flouted this guideline to such an extent (littering the site with inaccurate and unsound material which is still now coming to light) that we had to block him from contributing.

The same applies to definitions. --prime mover (talk) 10:11, 27 April 2024 (UTC)

The original statement didn't place any conditions on $k$ at all, it just listed the formula. I thought that the first proof only used Stirling's formula on wholly real applications of the Gamma function, but it seems I was mistaken. I'm reverting the edit. --CircuitCraft (talk) 17:31, 27 April 2024 (UTC)

You are right, I was mistaken in that I had not realised you had already entered the conditions as $\R \setminus \set {0, -1, 2, \ldots}$.

It may also apply to $\C \setminus \set {0, -1, 2, \ldots}$ as well, in which case one could enter the latter version as the main theorem and say "and here is the proof that applies only to $\R \setminus \set {0, -1, 2, \ldots}$" as an interesting curiosity. Bear in mind that, but for the published hint, it was actually my creation when I could do stuff like this. --prime mover (talk) 17:49, 27 April 2024 (UTC)