◀ ▲ ▶Branches / Combinatorics / Proposition: Factorial Polynomials vs. Polynomials
Proposition: Factorial Polynomials vs. Polynomials
Every factorial polynomial equals some "usual" polynomial, i.e. if $$\phi(x)=a_nx^{\underline{n}}+a_{n1}x^{\underline{n1}}+\ldots+a_1x^{\underline{1}}+a_0,\quad a_n\neq 0$$ is a factorial polynomial of degree $n$ then there are $b_n,\ldots,b_0\in C,$ such that $$\phi(x)=b_{n}x^{n}+b_{n1}x^{n1}+\ldots+b_{1}x+b_0,\quad b_n\neq 0$$
and vice versa.
Table of Contents
Proofs: 1
Mentioned in:
Definitions: 1
Solutions: 2
Thank you to the contributors under CC BYSA 4.0!
 Github:

References
Bibliography
 Miller, Kenneth S.: "An Introduction to the Calculus of Finite Differences And Difference Equations", Dover Publications, Inc, 1960