Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, an Appell sequence, named after Paul Emile Appell, is any polynomial sequence {pn(x)}n = 0, 1, 2, ... satisfying the identity, {d over dx} p_n(x) = np_{n-1}(x), and in which p0(x) is a non- zero constant. Among the most notable Appell sequences besides the trivial example { xn } 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.

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