超Bell多项式的一般性质——2-循环级数的Bell多项式
General Identities on Super Bell Polynomials —Bell polynomials of 2-recurring series
DOI: 10.12677/HANSPrePrints.2017.21018, PDF, 下载: 1,382  浏览: 3,906 
作者: 郭铭浩：上海交通大学生物医学工程学院，上海；郭志成：北方设计研究院，石家庄，河北
关键词: 普通（局部）Bell多项式；二次Bell多项式；超Bell多项式；二次线性Bell多项式；Partial Bell polynomial; second-order Bell polynomials; super Bell polynomials; second-order linear Bell Polynomial
摘要: 本文利用Bell多项式的维数定义，给出了与超Bell多项式等价的显式公式。它的逆关系也是最简单的2-循环级数的Taylor公式。利用给出的结论，解决了普通（局部）Bell多项式B_(n,k) (x_1,x_2,⋯,x_(n-k+1) )的计算问题。
Abstract: On using the symmetric defintion of Bell Polynomials, we deduce the explicitly by the formula for which the Super Bell Polynomials. Also, that determine some inverse relations and the connections with taylor formula of 2-recurring series. With this explicit computable expression, it is possible to easily evaluate B_(n,k) (x_1,x_2,⋯,x_(n-k+1)) directly for given values of n and k.
文章引用：郭铭浩, 郭志成. 超Bell多项式的一般性质——2-循环级数的Bell多项式[J]. 汉斯预印本, 2017, 2(1): 1-10. https://doi.org/10.12677/HANSPrePrints.2017.21018

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