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In mathematics, an Appell sequence, named after Paul Émile Appell, is any polynomial sequence { p n } n = 0 , 1 , 2 , … {\displaystyle \{p_{n}\}_{n=0,1,2,\ldots }} satisfying the identity
and in which p 0 {\displaystyle p_{0}} 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. Appell sequences have a probabilistic interpretation as systems of moments.