- Method of differences due to Pascal
- discrete calculus analog of the fact that the nth degree Taylor expansion of a polynomial is the polynomials.
- The first lemma is a direct consequence of the method of finite differences; it says that the nth forward difference of a polynomial of degree n-1 is identically zero. The inner summation in the second identity is basically computing the coefficients of the Newton Form of the polynomial, although you seem to be using a slightly different basis. Nevertheless, these results are quite standard.
Authors of those comments (and others who know stuff)--- please email me more exact references. I found some things on Google but it would be good to know what to read and what is a good source to reference. Preferable online.QUESTION: In a paper if you are using a result that is known how much detail should you put in?
- Clearly put in that it is known and provide a references. I would not want to frustrate my readers with This is easily derived from the method of differences. without providing a reference. In this day and age an online reference if you can mange it.
- If the result is not quite written down anywhere but your readers could easily derive it using known techniques, then you do not need to supply a proof. But this is not as clear a statement as it sounds- it depends on how you define readers, easily, known, and technique.
- If the result is known but you have a cute proof of it which seems new (hard to tell) then what do you do?
- If the proof is short then I am more inclined to include it. If its an e-journal than length matters less. (This topic has been raised in a different form before---if Conferences proceedings are CD's then why have a page limit?)
- If there are no online references then I am more inclined to include a proof.
- My only real point here is that its a QUESTION- what is the cutoff for what is worth including? There is no one answer.