An Appell sequence is a Sheffer sequence for . Roman (1984, pp. 86-106)
summarizes properties of Appell sequences and gives a number of specific examples.
The sequence
is Appell for iff
(1)
for all
in the field
of field characteristic 0, and iff
(2)
(Roman 1984, p. 27). The Appell identity states that the sequence is an Appell sequence iff
(3)
(Roman 1984, p. 27).
The Bernoulli polynomials , Euler polynomials , and Hermite polynomials are
Appell sequences (in fact, more specifically, they are Appell
cross sequences ).
See also Appell Cross Sequence ,
Sheffer Sequence ,
Umbral
Calculus
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References Hazewinkel, M. (Managing Ed.). Encyclopaedia of Mathematics: An Updated and Annotated Translation of the Soviet "Mathematical
Encyclopaedia." Dordrecht, Netherlands: Reidel, pp. 209-210, 1988. Roman,
S. "Appell Sequences." §2.5 and §2 in The
Umbral Calculus. New York: Academic Press, pp. 17 and 26-28 and 86-106,
1984. Rota, G.-C.; Kahaner, D.; Odlyzko, A. "On the Foundations
of Combinatorial Theory. VIII: Finite Operator Calculus." J. Math. Anal.
Appl. 42 , 684-760, 1973. Referenced on Wolfram|Alpha Appell Sequence
Cite this as:
Weisstein, Eric W. "Appell Sequence."
From MathWorld --A Wolfram Web Resource. https://mathworld.wolfram.com/AppellSequence.html
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