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:
“We have defined a story as a narrative of events arranged in their time-sequence. A plot is also a narrative of events, the emphasis falling on causality. “The king died and then the queen died” is a story. “The king died, and then the queen died of grief” is a plot. The time sequence is preserved, but the sense of causality overshadows it.”
—E.M. (Edward Morgan)