一个三角矩阵之逆与Catalan数恒等式  

Inverse of a Triangular Matrix and Several Identities of Catalan Numbers

作　　者：祁锋 QI Feng(College of Mathematics,Inner Mongolia University for Nationalities,Tongliao 028043,China;School of Mathematical Sciences,Tianjin Polytechnic University,Tianjin 300389,China)

机构地区：[1]内蒙古民族大学数学学院,内蒙古通辽028043 [2]天津工业大学数学科学学院,天津300389

出　　处：《湖南理工学院学报（自然科学版）》2020年第2期1-11,22,共12页Journal of Hunan Institute of Science and Technology(Natural Sciences)

摘　　要：在简单介绍Catalan数和第二类Chebyshev多项式的基本知识后,以一种真实且自然的形式重新阐述研究过程,包括研究的动因,问题的产生,对问题答案的两种猜测,猜测的解决过程,由猜测的解答衍生出来的新结论,新成果与已知结果的比较等.这项研究的成果包括与第二类Chebyshev多项式和Catalan数相关的一个矩阵之逆、一个反演定理和几个恒等式.After Catalan numbers and Chebyshev polynomial of the second kind were introduced,the author tends to really and naturally state the process of a research,including its motivations,generating of related problems,two guesses on answers to problems,solving process of guesses,new results derived from answers to two guesses,comparisons of new results with related known results,and the like.The results in the research include the inverse of a lower triangular matrix,an inversion theorem,and several identities related to the Chebyshev polynomials of the second kind and the Catalan numbers.

关 键 词：第二类CHEBYSHEV多项式 CATALAN数 矩阵之逆 恒等式 猜测 超几何函数 反演定理 第二类Bell多项式 

分 类 号：O156.4[理学—数学] O157.1[理学—基础数学]