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 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. Every Appell sequence is a Sheffer sequence, but most Sheffer sequences are not Appell sequences.