Higher-order tangent and secant numbers
| Autor: | Cvijovic, Djurdje |
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| Rok vydání: | 2013 |
| Předmět: | |
| Zdroj: | Computers and Mathematics with Applications, 62 (2011) 1879-1886 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1016/j.camwa.2011.06.031 |
| Popis: | In this paper higher-order tangent numbers and higher-order secant numbers, ${\mathscr{T}(n,k)}_{n,k =0}^{\infty}$ and ${\mathscr{S}(n,k)}_{n,k =0}^{\infty}$, have been studied in detail. Several known results regarding $\mathscr{T}(n,k)$ and $\mathscr{S}(n,k)$ have been brought together along with many new results and insights and they all have been proved in a simple and unified manner. In particular, it is shown that the higher-order tangent numbers $\mathscr{T}(n,k)$ constitute a special class of the partial multivariate Bell polynomials and that $\mathscr{S}(n,k)$ can be computed from the knowledge of $\mathscr{T}(n,k)$. In addition, a simple explicit formula involving a double finite sum is deduced for the numbers $\mathscr{T}(n,k)$ and it is shown that $\mathscr{T}(n,k)$ are linear combinations of the classical tangent numbers $T_n$. Comment: 10 pages; published |
| Databáze: | arXiv |
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