帕斯卡三角中 $\pi$ 与 $e$ 的新呈现
组合数学
2023-02-20 v2
摘要
以下工作展示了常数 和 与帕斯卡三角及卢卡斯三角之间的新联系，这些联系通过斐波那契多项式及类似方法建立。此外，猜想了这两个著名常数与帕斯卡三角和卢卡斯三角各行之间的关系，以及一些其他重要的相关恒等式。
引用
@article{arxiv.2212.11149,
title = {New presences of $\pi$ and $e$ in Pascal's triangle},
author = {Mauricio Guevara V.},
journal= {arXiv preprint arXiv:2212.11149},
year = {2023}
}
备注
13 pages, 13 figures. Fixed a minor mistake in the proof of theorem 4 (whose claim remains true), added a new, more general theorem relating e and the Lucas polynomials, as well as a new conjecture concerning the shallow diagonals of Pascal's triangle and pi. Also added an identity that relates e and pi to the factorials of composite numbers. Fixed some minor errata