Some tridiagonal determinants related to central delannoy numbers, the chebyshev polynomials, and the fibonacci polynomials

被引：0
|
作者：
Qi, F. [1 ,2 ,3 ,4 ]
Čerňanová, V. [5 ]
Semenov, Y.S. [6 ]
机构：
[1] Institute of Mathematics, Henan Polytechnic University, Jiaozuo, China
[2] College of Mathematics, Inner Mongolia University for Nationalities, Tongliao, China
[3] College of Science, Tianjin Polytechnic University, China
[4] Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China, Chengdu, China
[5] Department of Mathematics and Computer Science, Faculty of Education, Trnava University, Priemy-selná 4, Trnava,918 43, Slovakia
[6] Applied Mathematics-1, Moscow State University of Railway Engineering, Moscow,127994, Russia
来源：
UPB Scientific Bulletin, Series A: Applied Mathematics and Physics | 2019年 / 81卷 / 01期
关键词：
Cauchy product - Central Delannoy number - Chebyshev polynomials - Fibonacci numbers - Fibonacci polynomials - Generating functions - Second kinds - Tridiagonal determinants - Tridiagonal matrices;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
In the paper, the authors give a motivation from central Delannoy numbers to a tridiagonal determinant, find a generating function for the tridiagonal determinant, prove several formulas for the tridiagonal determinant, discuss the inverse of the tridiagonal matrix, connect the tridiagonal determinant with the Chebyshev polynomials, the Fibonacci numbers and polynomials, and the Cauchy product of central Delannoy numbers, derive several formulas for the tridiagonal determinant and the second kind Chebyshev polynomials, review computation of general tridiagonal determinants, present two new formulas for computing general tridiagonal determinants, and generalize central Delannoy numbers and their Cauchy product. © 2019, Politechnica University of Bucharest. All rights reserved.
引用
收藏
页码：123 / 136
相关论文
共 50 条
  • [21] POLYNOMIALS RELATED TO GENERALIZED CHEBYSHEV POLYNOMIALS
    Djordjevic, Gospava B.
    FILOMAT, 2009, 23 (03) : 279 - 290
  • [22] Pell numbers and Fibonacci polynomials
    Seiffert, H. -J.
    Bruckman, Paul S.
    FIBONACCI QUARTERLY, 2006, 44 (02): : 189 - 191
  • [23] On Higher-Dimensional Fibonacci Numbers, Chebyshev Polynomials and Sequences of Vector Convergents
    Coffey, Mark W.
    Hindmarsh, James L.
    Lettington, Matthew C.
    Pryce, John D.
    JOURNAL DE THEORIE DES NOMBRES DE BORDEAUX, 2017, 29 (02): : 369 - 423
  • [24] Sums of finite products of Chebyshev polynomials of the second kind and of Fibonacci polynomials
    Kim, Taekyun
    Kim, Dae San
    Dolgy, Dmitry V.
    Park, Jin-Woo
    JOURNAL OF INEQUALITIES AND APPLICATIONS, 2018,
  • [25] δ-FIBONACCI AND δ-LUCAS NUMBERS, δ-FIBONACCI AND δ-LUCAS POLYNOMIALS
    Witula, Roman
    Hetmaniok, Edyta
    Slota, Damian
    Pleszczynski, Mariusz
    MATHEMATICA SLOVACA, 2017, 67 (01) : 51 - 70
  • [26] Remarks on Chebyshev polynomials, Fibonacci polynomials and Kauffman bracket skein modules
    Owczarek, Robert
    JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS, 2018, 27 (07)
  • [27] Sums of finite products of Chebyshev polynomials of the second kind and of Fibonacci polynomials
    Taekyun Kim
    Dae San Kim
    Dmitry V. Dolgy
    Jin-Woo Park
    Journal of Inequalities and Applications, 2018
  • [28] Representing derivatives of Chebyshev polynomials by Chebyshev polynomials and related questions
    Prodinger, Helmut
    OPEN MATHEMATICS, 2017, 15 : 1156 - 1160
  • [29] Some applications of the Chebyshev polynomials to polynomials in general
    Jameson, G. J. O.
    MATHEMATICAL GAZETTE, 2025, 109 (574): : 93 - 100
  • [30] Binomial Fibonacci Sums from Chebyshev Polynomials
    Adegoke, Kunle
    Frontczak, Robert
    Goy, Taras
    JOURNAL OF INTEGER SEQUENCES, 2023, 26 (09)
12345