In mathematics, an Appell sequence, named after Paul Émile Appell, is any polynomial sequence {pn(x)}n = 0, 1, 2, ... satisfying the identity
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.
Read more about Appell Sequence: Equivalent Characterizations of Appell Sequences, Recursion Formula, Subgroup of The Sheffer Polynomials, Different Convention
Famous quotes containing the word sequence:
“Reminiscences, even extensive ones, do not always amount to an autobiography.... For autobiography has to do with time, with sequence and what makes up the continuous flow of life. Here, I am talking of a space, of moments and discontinuities. For even if months and years appear here, it is in the form they have in the moment of recollection. This strange formit may be called fleeting or eternalis in neither case the stuff that life is made of.”
—Walter Benjamin (18921940)