Commutation Relations, Normal Ordering, and Stirling Numbers
Commutation Relations, Normal Ordering, and Stirling Numbers
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DOI：
10.1201/b18869
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发表时间：
2015-09
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影响因子：
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通讯作者：
T. Mansour;M. Schork
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文献类型：
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作者：
T. Mansour;M. Schork
引言集合划分、斯特林和贝尔数交换关系和算子排序Weyl代数和相关内容书中的正常排序基本工具序列求解递归关系生成函数组合结构Riordan阵列和Sheffer序列斯特林和贝尔数斯特林和贝尔数的定义和基本性质贝尔数的进一步性质q变形斯特林和贝尔数（p，q）-变形斯特林数和Bell数斯特林数的推广广义斯特林数作为运算关系式中展开系数的Hsu和Shiue的斯特林数：斯特林数的大统一变形和Hsu，Shiue关于斯特林数的其他推广与正规序Weyl代数初级量子力学简介正规序的物理方面Weyl代数中的正规序Weyl代数中的其他方面正常排序Wick定理单性原理与组合结构的进一步联系一系列运算符排序方案多模式情况q-变形Weyl代数和亚纯Weyl代数关于q-交换变量的评论q-变形Weyl代数亚纯Weyl代数q-亚纯Weyl代数Weyl代数定义和文献正规序在特殊Ore扩张中的推广广义Weyl代数正规序的基本观察与斯特林和Bell数相关的q-变形广义Weyl代数定义及文献基本观察与斯特林数和Bell数相关的二项式公式任意多项式的推广顺序展望：Touchard函数的真实的顺序展望：ComtetTouchard函数展望：q变形广义Touchard多项式附录书目索引练习出现在每章的末尾。
Introduction Set Partitions, Stirling, and Bell Numbers Commutation Relations and Operator Ordering Normal Ordering in the Weyl Algebra and Relatives Content of the Book Basic Tools Sequences Solving Recurrence Relations Generating Functions Combinatorial Structures Riordan Arrays and Sheffer Sequences Stirling and Bell Numbers Definition and Basic Properties of Stirling and Bell Numbers Further Properties of Bell Numbers q-Deformed Stirling and Bell Numbers (p, q)-Deformed Stirling and Bell Numbers Generalizations of Stirling Numbers Generalized Stirling Numbers as Expansion Coefficients in Operational Relations Stirling Numbers of Hsu and Shiue: A Grand Unification Deformations of Stirling Numbers of Hsu and Shiue Other Generalizations of Stirling Numbers The Weyl Algebra, Quantum Theory, and Normal Ordering The Weyl Algebra Short Introduction to Elementary Quantum Mechanics Physical Aspects of Normal Ordering Normal Ordering in the Weyl Algebra-Further Aspects Normal Ordering in the Weyl Algebra Wick's Theorem The Monomiality Principle Further Connections to Combinatorial Structures A Collection of Operator Ordering Schemes The Multi-Mode Case The q-Deformed Weyl Algebra and the Meromorphic Weyl Algebra Remarks on q-Commuting Variables The q-Deformed Weyl Algebra The Meromorphic Weyl Algebra The q-Meromorphic Weyl Algebra A Generalization of the Weyl Algebra Definition and Literature Normal Ordering in Special Ore Extensions Basic Observations for the Generalized Weyl Algebra Aspects of Normal Ordering Associated Stirling and Bell Numbers The q-Deformed Generalized Weyl Algebra Definition and Literature Basic Observations Binomial Formula Associated Stirling and Bell Numbers A Generalization of Touchard Polynomials Touchard Polynomials of Arbitrary Integer Order Outlook: Touchard Functions of Real Order Outlook: ComtetTouchard Functions Outlook: q-Deformed Generalized Touchard Polynomials Appendices Bibliography Indices Exercises appear at the end of each chapter.