文章详细信息 关键词： 矩阵多项式;;特征多项式;;母函数;;矩阵函数 [gap=227]Keywords: matrix polynomial;characteristic polynomial;generating functions;matrix functions
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Recurrence Relations and Generating Functions 生成函数 ; 递推关系和生成函数
ratio of generating functions 生发函数比
product of generating functions 生成函数积
conditional moment generating functions 条件矩母函数的
moment generating functions 矩母函数
moment-generating functions 矩生成函数
minimal generating functions 最小生成函数
probability generating functions 概率母函数
autocovariance generating functions 自协方差发生函数
Many important results were obtained especially after using generating functions and calculus.
特别是应用生成函数与微积分之后,取得了相当一批重要的成果。
参考来源 - 欧拉数与伯努利数的历史发展Based on partitions of finite sets and restrictions to the distances among the elements in each part, we generalize Stirling numbers of the second kind in two different ways. The recurrence relations, generating functions and explicit formulae are established consequently.
4．以有限集分拆为出发点，通过限制每个块中元素的距离，我们以两种方式推广了第二类Stirling数，建立了它们的递归关系、发生函数以及显式表达式，并提供了几个组合解释。
参考来源 - 反演技巧在组合恒等式中的应用·2,447,543篇论文数据，部分数据来源于NoteExpress
Generating functions are an ideal tool for studying sequences defined by recurrence.
母函数是研究用递推关系来确定的函数的最理想工具。
In this paper, the general high order equal ratios sequence have been studied by generating functions and recursion relations.
本文利用母函数和递推关系求解一般高阶等比序列，得到了这类序列的一般解。
To study combinatorial properties of discrete sequences by means of zeros of generating functions is an important topic in combinatorics.
通过发生函数的零点来研究离散序列的组合性质是组合学中的一个重要课题。
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