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Show that if $ p $ is an $ n $th-degree polynomial, then

$ p(x + 1) = \sum_{i = 0}^n \frac {p^{(i)} (x)}{i!} $

$\sum_{i=0}^{n} \frac{p^{(i)}(x)}{i !}$

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Campbell University

Oregon State University

Harvey Mudd College

Baylor University

so show that it is a death grip polynomial than Pierre. It's plus one equals our friend zero to end the eye ther with appear That's over five pictorial. All right, so this is just a tale experience. So we recorded at peace and degree polynomial So which means Sochi I axe because zero, when I is greater than I am is end in danger. Next number, actually. So that means the Incas worth reading of P of X equals good off the off the like the tail. So the tale of p of X, the tail with him appear mats is gonna be zero for all I greater than n So we can We want this room as I'm from zero to infinity The threat of p of X over equatorial tons X plus one minus x Sorry at first one one is axe to horrify I So what is this is just a tailor experience. It's just a teller experience at X Yeah, it just takes parent attacks. So this is just equals two p experts one, because the convergence the reader of convergence for this function is just you just are the horror line. So this is finally was too. Because this or act or it comes. So this one to our eye. And I's in here from zero to me, seriously. One. Just because two people of a swell fine definition the tailor Siri's if they hear experience and so that s all right.

University of Illinois at Urbana-Champaign