The Legendre–Stirling numbers
| Autor: | George E. Andrews, Lance L. Littlejohn, Wolfgang Gawronski |
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| Rok vydání: | 2011 |
| Předmět: |
Discrete mathematics
Mathematics::Combinatorics Recurrence relation Stirling numbers of the first kind Large numbers Stirling numbers of the second kind Theoretical Computer Science Combinatorics Euler criterion Stirling number Discrete Mathematics and Combinatorics Legendre–Stirling numbers Algebraic number Left-definite theory Bernoulli number Real number Mathematics |
| Zdroj: | Discrete Mathematics. 311(14):1255-1272 |
| ISSN: | 0012-365X |
| DOI: | 10.1016/j.disc.2011.02.028 |
| Popis: | The Legendre–Stirling numbers are the coefficients in the integral Lagrangian symmetric powers of the classical Legendre second-order differential expression. In many ways, these numbers mimic the classical Stirling numbers of the second kind which play a similar role in the integral powers of the classical second-order Laguerre differential expression. In a recent paper, Andrews and Littlejohn gave a combinatorial interpretation of the Legendre–Stirling numbers. In this paper, we establish several properties of the Legendre–Stirling numbers; as with the Stirling numbers of the second kind, they have interesting generating functions and recurrence relations. Moreover, there are some surprising and intriguing results relating these numbers to some classical results in algebraic number theory. |
| Databáze: | OpenAIRE |
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