On dual hyperbolic numbers with generalized Jacobsthal numbers components

SOYKAN Y., TAŞDEMİR E., OKUMUŞ İ.

INDIAN JOURNAL OF PURE & APPLIED MATHEMATICS, cilt.54, sa.3, ss.824-840, 2023 (SCI-Expanded, Scopus) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 54 Sayı: 3
  • Basım Tarihi: 2023
  • Doi Numarası: 10.1007/s13226-022-00301-1
  • Dergi Adı: INDIAN JOURNAL OF PURE & APPLIED MATHEMATICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, INSPEC, zbMATH
  • Sayfa Sayıları: ss.824-840
  • Anahtar Kelimeler: Jacobsthal numbers, Jacobsthal-Lucas numbers, Dual hyperbolic numbers, Dual hyperbolic Jacobsthal numbers, Cassini identity, PELL
  • İstanbul Üniversitesi-Cerrahpaşa Adresli: Evet

Özet

In this paper, we introduce the generalized dual hyperbolic Jacobsthal numbers. As special cases, we deal with dual hyperbolic Jacobsthal and dual hyperbolic Jacobsthal-Lucas numbers. We present Binet's formulas, generating functions and the summation formulas for these numbers. Moreover, we give Catalan's, Cassini's, d'Ocagne's, Gelin-Cesaro's, Melham's identities and present matrices related with these sequences.