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

Creative Commons License

Kilic E., ÖMÜR N., KOPARAL S.

HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS, cilt.49, sa.2, ss.684-694, 2020 (SCI-Expanded) identifier identifier

  • 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
  • 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.