Baxter algebras and the umbral calculus

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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 the Baxter algebra. This characterization leads to a natural generalization of the umbral calculus that includes the classical umbral calculus in a family of λ-umbral calculi parameterized by λ in the base ring.

Original languageEnglish (US)
Pages (from-to)405-426
Number of pages22
JournalAdvances in Applied Mathematics
Issue number2-3
StatePublished - 2001

All Science Journal Classification (ASJC) codes

  • Applied Mathematics


  • Baxter algebra
  • Binomial type
  • Divided power
  • Umbral algebra
  • Umbral calculus

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