Umbral Calculus

Introduction I’ll start by rationalizing an example of “old” umbral calculus from Wikipedia . |\newcommand{pair}[2]{\langle{#1}\mid{#2}\rangle}| |\newcommand{bigpair}[2]{\left\langle{#1}\ \middle|\ {#2}\right\rangle}| |\newcommand{pseq}[2]{\{#1\}_{#2 \in \mathbb N}}| |\newcommand{ucomp}[2]{#1_n(\underline #2(x))}| We know |(x+y)^n = \sum_{k=0}^n {n \choose k} x^{n-k} y^k|. We then “infer” that…