SPLIT (s, t)−LUCAS QUATERNIONS

Yıl 2024, Cilt: 7 Sayı: To memory "Assoc. Prof. Dr. Zeynep AKDEMİRCİ ŞANLI", 1 - 9, 29.12.2024

Hamza Menken , Durdane Tekin

https://doi.org/10.33773/jum.1549438

Öz

In this paper, we introduce a new class of split (s,t)- Lucas quaternions that generalizes the split Lucas quaternions. Additionally, we derive Binet-like formulas, generating functions, binomial sums and Honsberger-like, d'Ocagne-like, Catalan's-like and Cassini's-like identities.

Anahtar Kelimeler

Lucas numbers , quaternions , binomial sums , Binet formula.

Kaynakça

• M. Akyigit, H.H. Kosal, M. Tosun, Split Fibonacci Quaternions, Advances in Applied Clifford Algebras, Vol.23, No.3, pp.535-545, (2013).
• T. Koshy, Fibonacci and Lucas numbers with Applications, Wiley, (2019).
• G. Lee, M. Asci, Some Properties of the (p,q)- Fibonacci and (p,q)-Lucas Polynomials, Journal of Applied Mathematics, (2012).
• A. Ipek, On (p, q)-Fibonacci Quaternions and Their Binet Formulas, Generating Functions and Certain Binomial Sums, Advances in Applied Clifford Algebras, Vol.27, No.2, pp.1343-1351, (2017).
• B.K. Patel, P.K. Ray, On The Properties Of (p,q)-Fibonacci and (p,q)-Lucas Quaternions, Article in Mathematical Reports, 244, (2016).
• S. Halici, On Fibonacci Quaternions, Advances in Applied Clifford Algebras, Vol.22, No.2, pp.321-327, (2012).
• A. Suvarnamani, Some Properties of (p, q)-Lucas Number, Kyungpook Mathematical Journal, Vol.56, No.2, pp.367–370, (2016).
• O. Diskaya, H. Menken, On the Split (s, t)-Padovan and (s, t)-Perrin Quaternions, International Journal of Applied Mathematics and Informatics, Vol.13, pp.25-28, (2019).
• O. Diskaya, H. Menken, P.M.M.C. Catarino, On the Hyperbolic Leonardo and Hyperbolic Francois Quaternions, Journal of New Theory, Vol.42, pp.74-85, (2023).
• O. Diskaya, H. Menken, On the Pseudo-Fibonacci and Pseudo-Lucas Quaternions, Electronic Journal of Mathematical Analysis and Applications, Vol.12, No.1, pp.1-9, (2024).
• O. Diskaya, H. Menken, The m-Order Linear Recursive Quaternions, Journal of Contemporary Applied Mathematics, Vol.13, No.2, (2023).
• O. Diskaya, Split (p, q)-fibonacci Kuaterniyonları ve Oktonyonları, Master's thesis, Karamanoglu Mehmetbey Universitesi, (2017).
• O. Diskaya, H. Menken, On the (s, t)-Padovan and (s, t)-Perrin Quaternions, J. Adv. Math. Stud., Vol.12, pp.186–192, (2019).
• O. Diskaya, H. Menken, On the (p, q)-Fibonacci N-dimensional Recurrences, Bulletin ofthe International Mathematical Virtual Institute, Vol.12, No.2, pp.205-212, (2022).
• M. Erdogdu, M. Ozdemir, On Complex Split Quaternion Matrices, Advances in Applied Clifford Algebras, Vol.23, pp.625-638, (2013).
• Y. Alagoz, K.H. Oral, S. Yuce, Split Quaternion Matrices, Miskolc Mathematical Notes, Vol.13, No.2, pp.223-232, (2012).
• E. Polatli, C. Kizilates, S. Kesim, On Split k-Fibonacci and k-Lucas Quaternions, Advances in Applied Clifford Algebras, Vol.26, pp.353-362, (2016).
• U. Tokeser, Z. Unal, G. Bilgici, Split Pell and Pell–Lucas Quaternions, Advances in Applied Clifford Algebras, Vol.27, pp.1881-1893, (2017).
• F. Babadag, M.M. Kakar, A. Atasoy, A New Approach to Dual Jacobsthal Split Quaternions with Different Polar Representation, Journal of Advances in Mathematics and Computer Science, Vol.39, No.2, pp.52-62, (2024).
• C.B. Cimen, A. Ipek, On Pell Quaternions and Pell-Lucas Quaternions, Advances in Applied Clifford Algebras, Vol.26, pp.39-51, (2016).
• D. Tasci, Padovan and Pell-Padovan Quaternions, Journal of Science and Arts, Vol.42, No.1, pp.125-132, (2018).