Abstract
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 language | English (US) |
|---|---|
| Pages (from-to) | 405-426 |
| Number of pages | 22 |
| Journal | Advances in Applied Mathematics |
| Volume | 27 |
| Issue number | 2-3 |
| DOIs | |
| State | Published - 2001 |
All Science Journal Classification (ASJC) codes
- Applied Mathematics
Keywords
- Baxter algebra
- Binomial type
- Divided power
- Umbral algebra
- Umbral calculus