论文标题
关于双变量的多晶型多项式
On bi-variate poly-Bernoulli polynomials
论文作者
论文摘要
我们使用我们在先前的工作中研究的第二种数字的概括在两个变量中介绍了两个变量的多项式。我们证明了标准Bernoulli多项式的一些已知结果的双变量多bernoulli多项式版本，作为加法公式和二项式公式。我们还证明了一个结果，使我们能够从多项式身份获得多项式多项式身份，并且我们使用此结果获得了涉及多伯努利和/或标准Bernoulli多项式产品的几种身份。我们证明了两种综合复发，用于双变量的多晶型啤酒多项式，并从中获得一些推论。
We introduce poly-Bernoulli polynomials in two variables by using a generalization of Stirling numbers of the second kind that we studied in a previous work. We prove the bi-variate poly-Bernoulli polynomial version of some known results on standard Bernoulli polynomials, as the addition formula and the binomial formula. We also prove a result that allows us to obtain poly-Bernoulli polynomial identities from polynomial identities, and we use this result to obtain several identities involving products of poly-Bernoulli and/or standard Bernoulli polynomials. We prove two generalized recurrences for bi-variate poly-Bernoulli polynomials, and obtain some corollaries from them.
