论文标题
构建莱布尼兹数字及其特性的概括
Construction of a generalization of the Leibnitz numbers and their properties
论文作者
论文摘要
本文的目的是对莱布尼茨数字的新概括从β函数应用于伯恩斯坦基函数的修改中得出。我们还借助了莱布尼茨数字的一些属性，这些属性借助了其生成功能，这些功能源自$ p $ - 亚种整数集合的Volkenborn积分。我们还提供了一些新颖的身份和关系，涉及莱布尼茨数字，daehee数量，changhee数，逆二项式系数和组合总和。最后，通过对Mathematica 12.0中Leibnitz数字概括的计算公式及其实现，我们用表格计算了这些数字的几个值。最后，通过使用Volkenborn积分与Mahler系数的应用，我们得出了一些涉及Leibnitz数字的新公式。
The aim of this paper is to give a novel generalization of the Leibnitz numbers derived from application of the Beta function to the modification for the Bernstein basis functions. We also give some properties of the Leibnitz numbers with the aid of their generating functions derived from the Volkenborn integral on the set of $p$-adic integers. We also give some novel identities and relations involving the Leibnitz numbers, the Daehee numbers, the Changhee numbers, inverse binomial coefficients, and combinatorial sums. Finally, by coding computation formula for the generalization of the Leibnitz numbers in Mathematica 12.0 with their implementation, we compute few values of these numbers with their tables. Finally, by using the applications of Volkenborn integral to Mahler coefficients, we derive some novel formulas involving the Leibnitz numbers.
