Uniform Convergence Behavior of the Bernoulli Polynomials
| dc.creator | Mangual, John | |
| dc.date | 2007-03-15 | |
| dc.date.accessioned | 2026-07-07T07:52:06Z | |
| dc.date.available | 2026-07-07T07:52:06Z | |
| dc.description | The roots of Bernoulli polynomials, $B_n(z)$, when plotted in the complex plane, accumulate around a peculiar H-shaped curve. Karl Dilcher proved in 1987 that, on compact subsets of $\mathbb{C}$, the Bernoulli polynomials asymptotically behave like sine or cosine. Here we establish the asmptotic behavior of $B_n(nz)$, compute the distribution of real roots of Bernoulli polynomials and show that, properly rescaled, the complex roots lie on the curve $e^{- 2π\text{Im}(z)} = 2πe |z|$ or $e^{2π\text{Im}(z)}= 2πe |z|$. | |
| dc.description | 8pages, 3 figures. To be submitted | |
| dc.identifier | https://arxiv.org/abs/math/0703452 | |
| dc.identifier | http://arxiv.org/abs/math/0703452 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/125759 | |
| dc.subject | Classical Analysis and ODEs | |
| dc.title | Uniform Convergence Behavior of the Bernoulli Polynomials | |
| dc.type | text |