New analogues of the Filbert and Lilbert matrices via products of two k-tuples asymmetric entries
HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS, vol.49, no.2, pp.684-694, 2020 (SCI-Expanded, Scopus, TRDizin)
- Publication Type: Article / Article
- Volume: 49 Issue: 2
- Publication Date: 2020
- Doi Number: 10.15672/hujms.473495
- Journal Name: HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, zbMATH, TR DİZİN (ULAKBİM)
- Page Numbers: pp.684-694
- Keywords: generalized Filbert matrix, q-analogues, LU-decomposition, Zeilberger's algorithm, computer algebra system (CAS), GENERALIZED FIBONACCI MATRIX, DETERMINANT
- Open Archive Collection: AVESIS Open Access Collection
- Bursa Uludag University Affiliated: No
Abstract
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.