Bernoulli polynomials and Pascal matrices in the context of Clifford analysis
| Autor: | Graça Tomaz, Helmuth R. Malonek |
|---|---|
| Rok vydání: | 2009 |
| Předmět: |
Discrete mathematics
Block Pascal matrix Mathematics::Complex Variables Applied Mathematics Clifford algebra Hypercomplex analysis Clifford analysis Bernoulli polynomials Hypercomplex Bernoulli polynomials symbols.namesake Multiplication theorem symbols Hypercomplex Bernoulli matrix Discrete Mathematics and Combinatorics Bernoulli scheme Bernoulli process Bernoulli number Bernoulli numbers Mathematics |
| Zdroj: | Discrete Applied Mathematics. 157(4):838-847 |
| ISSN: | 0166-218X |
| DOI: | 10.1016/j.dam.2008.06.009 |
| Popis: | This paper describes an approach to generalized Bernoulli polynomials in higher dimensions by using Clifford algebras. Due to the fact that the obtained Bernoulli polynomials are special hypercomplex holomorphic (monogenic) functions in the sense of Clifford Analysis, they have properties very similar to those of the classical polynomials. Hypercomplex Pascal and Bernoulli matrices are defined and studied, thereby generalizing results recently obtained by Zhang and Wang (Z. Zhang, J. Wang, Bernoulli matrix and its algebraic properties, Discrete Appl. Math. 154 (11) (2006) 1622–1632). |
| Databáze: | OpenAIRE |
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