Mathematics – Rings and Algebras
Scientific paper
2004-07-09
Adv. in Appl. Math. 27 (2001), 405-426
Mathematics
Rings and Algebras
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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