一个推广的Leibnitz数的构造及其性质
Construction of a generalization of the Leibnitz numbers and their properties
摘要：
将β函数应用于Bernstein基函数的修正，给出了Leibnitz数的一个新的推广.借助于由$p$ -adic整数集上的Volkenborn积分导出的Leibnitz数的生成函数，给出了Leibnitz数的一些性质.我们也给出了一些新的身份和关系涉及的Leibnitz数，Daehee数，Changhee数，逆二项式系数，和组合和。最后，通过在Mathematica 12.0中编写推广的莱布尼茨数的计算公式及其实现，利用其表计算出这些数的几个值。最后，利用Volkenborn积分在Mahler系数上的应用，得到了一些新的包含Leibnitz数的公式.
英文摘要：
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.
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