oliadas73

2022-10-09

Making sense of this formula relating to polynomials :

$P(x+n+1)=\sum _{i=0}^{n}(-1{)}^{n-1}{\textstyle (}\genfrac{}{}{0ex}{}{n+1}{i}{\textstyle )}P(x+i)$

$P(x+n+1)=\sum _{i=0}^{n}(-1{)}^{n-1}{\textstyle (}\genfrac{}{}{0ex}{}{n+1}{i}{\textstyle )}P(x+i)$

lascosasdeali3v

Beginner2022-10-10Added 10 answers

"If you take the right side over to the left (correcting a minor typo - ""n-1"" should be ""n-i"" in the power of -1), the equation can also be written like this:

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What this is, is actually the iterated difference. That is, if $$

$$

What this is, is actually the iterated difference. That is, if $$

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