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Date: 24-12-2019
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Date: 7-12-2020
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Date: 16-8-2020
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A sequence
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where is a Sheffer sequence,
is invertible, and
ranges over the real numbers. If
is an associated Sheffer sequence, then
is called a cross sequence. If
, then
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is called an Appell cross sequence.
An example is the Laguerre polynomial.
REFERENCES:
Brown, J. W. and Goldberg, J. L. "A Note on Generalized Appell Polynomials." Amer. Math. Monthly 75, 169-170, 1968.
Roman, S. "Cross Sequences and Steffensen Sequences." §5.3 in The Umbral Calculus. New York: Academic Press, pp. 140-143, 1984.
Rota, G.-C.; Kahaner, D.; and Odlyzko, A. "On the Foundations of Combinatorial Theory VIII: Finite Operator Calculus." J. Math. Anal. Appl. 42, 684-760, 1973.
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