Appell sequence
In mathematics, an Appell sequence, named after Paul Émile Appell, is any polynomial sequence { p n ( x ) } n = 0 , 1 , 2 , … {\displaystyle \{p_{n}(x)\}_{n=0,1,2,\ldots }} satisfying the identity d d x p n ( x ) = n p n − 1 ( x ) , {\displaystyle {\frac {d}{dx}}p_{n}(x)=np_{n-1}(x),} and in which p 0 ( x ) {\displaystyle p_{0}(x)} is a non-zero constant. Among the most notable Appell sequences besides the trivial example { x n } {\displaystyle \{x^{n}\}} are the Hermite polynomials, the Bernoulli polynomials, and the Euler polynomials.