The inverse of a triangular matrix and several identities of the Catalan numbers

Applicable Analysis and Discrete Mathematics

article

Feng Qi¹  Qing Zou²  Bai-Ni Guo³ 

[1] College of Mathematics Inner Mongolia University for Nationalities Tongliao 028043 Inner Mongolia, China School of Mathematical Sciences Tianjin Polytechnic University Tianjin 300387;Department of Mathematics The University of Iowa IA 52242;School of Mathematics and Informatics Henan Polytechnic University Jiaozuo 454010 Henan

关键词: Chebyshev polynomials of the second kind;    inverse matrix;    Catalan number;    Generating function;    integral representation;   

DOI  :  10.2298/AADM190118018Q

学科分类：社会科学、人文和艺术（综合）

来源: Univerzitet u Beogradu * Elektrotehnicki Fakultet / University of Belgrade, Faculty of Electrical Engineering

【 摘 要 】

In the paper, the authors establish two identities to express higher orderderivatives and integer powers of the generating function of the Chebyshevpolynomials of the second kind in terms of integer powers and higher order derivatives of the generating function of the Chebyshev polynomials ofthe second kind respectively, find an explicit formula and an identity for theChebyshev polynomials of the second kind, conclude the inverse of an integer,unit, and lower triangular matrix, derive an inversion theorem, present several identities of the Catalan numbers, and give some remarks on the closelyrelated results including connections of the Catalan numbers with the Chebyshev polynomials of the second kind, the central Delannoy numbers, and theFibonacci polynomials respectively.

【 授权许可】

Unknown