论文标题
涉及二项式系数，双重和上升阶乘及其概率的解释和证明的多项式身份
Polynomial identities that involve binomial coefficients, double and rising factorials and their probabilistic interpretations and proofs
论文作者
论文摘要
我们制定了几种多项式身份。这些身份的一侧具有一个不错的简单形式。而另一种具有多项式的形式，其系数包含二项式系数双重阶乘或（和）上升的阶乘。这些身份的起源和证据是概率的。但是，它们的形式提出了简化表达式的普遍应用。续集中介绍了许多有用的简化公式。
We formulate several polynomial identities. One side of these identities has a nice simple form. Whereas the other has a form of a polynomial whose coefficients contain binomial coefficients double factorials or (and) rising factorials. The origins and the proofs of these identities are probabilistic. However, their form suggests universal applications in simplifying expressions. Many useful simplifying formulae are presented in the sequel.
