Pascal函数矩阵的进一步推广及应用  

Further Generalization of Pascal Functional Matrix and Applications

作　　者：赵熙强[1] 李琳[1] 

机构地区：[1]中国海洋大学数学科学学院,山东青岛266100

出　　处：《中国海洋大学学报（自然科学版）》2015年第3期136-140,共5页Periodical of Ocean University of China

摘　　要：通过改变矩阵元素得到Pascal函数矩阵的一种推广形式Pn[f(t)],运用矩阵相关理论讨论其代数性质及指数展开形式,由Pn[f(t)]的逆给出1个反演关系,借助指数发生函数,得到包含二项式型多项式、Hermite多项式与Euler多项式等的一些组合恒等式;最后,给出了Pn[f(t)]的2种不同形式的推广。A generalized form of Pascal functional matrix denoted as Pn[f（t）]is established by changing the elements of the matrix,and its algebraic properties and exponential representation are discussed by using the relevant theories of matrix.An inverse relation is obtained from the inverse of Pn[f（t）],and then some combinatorial identities involving the polynomial of binomial type,Hermite polynomial and Euler polynomial are obtained by using the exponential generating functions;Finally,our study is further extended through giving two different generalizations of Pn[f（t）].

关 键 词：Pascal函数矩阵 下三角矩阵 组合恒等式 反演 

分 类 号：O157.1[理学—数学]