New analogues of the Filbert and Lilbert matrices via products of two k-tuples asymmetric entries
HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS, cilt.49, sa.2, ss.684-694, 2020 (SCI-Expanded, Scopus, TRDizin)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 49 Sayı: 2
- Basım Tarihi: 2020
- Doi Numarası: 10.15672/hujms.473495
- Dergi Adı: HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, zbMATH, TR DİZİN (ULAKBİM)
- Sayfa Sayıları: ss.684-694
- Anahtar Kelimeler: generalized Filbert matrix, q-analogues, LU-decomposition, Zeilberger's algorithm, computer algebra system (CAS), GENERALIZED FIBONACCI MATRIX, DETERMINANT
- Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
- Bursa Uludağ Üniversitesi Adresli: Hayır
Özet
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.