Baxter Algebras and Umbral Calculus

Mathematics – Rings and Algebras

Scientific paper

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22 pages

Scientific paper

We apply recent constructions of free Baxter algebras to the study of the
umbral calculus. We give a characterization of the umbral calculus in terms of
Baxter algebra. This characterization leads to a natural generalization of the
umbral calculus that include the classical umbral calculus in a family of
$\lambda$-umbral calculi parameterized by $\lambda$ in the base ring.

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