CAJ | 학술논문

在讨论组合恒等式时通常采用组合方法，如取系数法、Riordan阵法等，作为基本研究工具。在本文中我们运用比较少见的一种方法来研究了一些特殊组合序列的恒等式。特别的，我们根据前人得出的一些组合序列的概率表达式，利用数学期望的性质、二项式恒等式以及多项式恒等式等方法，得到了有关两类Stirling数、二项式系数倒数、调和数、Bell数以及错排数的一些新的恒等式。
재토론조합항등식시통상채용조합방법，여취계수법、Riordan진법등，작위기본연구공구。재본문중아문운용비교소견적일충방법래연구료일사특수조합서렬적항등식。특별적，아문근거전인득출적일사조합서렬적개솔표체식，이용수학기망적성질、이항식항등식이급다항식항등식등방법，득도료유관량류Stirling수、이항식계수도수、조화수、Bell수이급착배수적일사신적항등식。
In many cases we can use combinatorial methods, e.g., the coe?cient method and the Riordan arrays etc., to prove combinatorial identities. In this paper, by making use of some unusual techniques, we achieve some specific combinatorial identities. Specifically, we derive some new identities involving two kinds of Stirling numbers, reciprocal of binomial coe?cient, harmonic numbers, Bell numbers and the number of derangements, by utilizing given probability expressions, properties of mathematical expectation, binomial identities and polynomial identities.