New analogues of the Filbert and Lilbert matrices via products of two k-tuples asymmetric entries

被引：1

作者：

Kilic, Emrah ^{[1
]}

Omur, Nese ^{[2
]}

Koparal, Sibel ^{[2
]}

机构：

[1] TOBB Univ Econ & Technol, Dept Math, TR-06560 Ankara, Turkey

[2] Kocaeli Univ, Dept Math, TR-41380 Kocaeli, Turkey

来源：

HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS | 2020年 / 49卷 / 02期

关键词：

generalized Filbert matrix; q-analogues; LU-decomposition; Zeilberger's algorithm; computer algebra system (CAS); GENERALIZED FIBONACCI MATRIX; DETERMINANT;

D O I：

10.15672/hujms.473495

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we present new analogues of the Filbert and Lilbert matrices via products of two k-tuples asymmetric entries consist of the Fibonacci and Lucas numbers. We shall derive explicit formulae for their LU-decompositions and inverses. To prove the claimed results, we write all the identities to be proven in q-word and then use the celebrated Zeilberger algorithm to prove required q-identities.

引用

页码：684 / 694

页数：11

共 3 条

[1] NEW FILBERT AND LILBERT MATRICES WITH ASYMMETRIC ENTRIES
Bozdag, Hacer
Kilic, Emrah
Akkus, Ilker
[J]. MATHEMATICA SLOVACA, 2020, 70 (02) : 289 - 296
[2] New asymmetric generalizations of the Filbert and Lilbert matrices
Emrah Kılıç
Sibel Koparal
Neşe Ömür
[J]. Periodica Mathematica Hungarica, 2019, 78 : 231 - 241
[3] New asymmetric generalizations of the Filbert and Lilbert matrices
Kilic, Emrah
Koparal, Sibel
Omur, Nese
[J]. PERIODICA MATHEMATICA HUNGARICA, 2019, 78 (02) : 231 - 241

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