Using an operator ordering method for some commutative superposition operators, we introduce two new multi-variable special polynomials and their generating functions, and present some new operator identities and integral formulas involving the two special polynomials. Instead of calculating complicated partial differential, we use the special polynomials and their generating functions to concisely address the normalization, photocount distributions and Wigner distributions of several quantum states that can be realized physically, the results of which provide real convenience for further investigating the properties and applications of these states.

中文翻译：

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使用运算符排序方法的多变量特殊多项式

通过对一些可交换叠加算子使用算子排序方法，我们介绍了两个新的多变量特殊多项式及其生成函数，并给出了涉及这两个特殊多项式的一些新的算子恒等式和积分公式。无需计算复杂的偏微分，而是使用特殊的多项式及其生成函数来简明地解决可以物理实现的几种量子态的归一化，光数分布和Wigner分布，其结果为进一步研究性质和性能提供了真正的便利。这些状态的应用。