On Hybrid numbers with Gaussian Mersenne Coefficients

Öz

On Hybrid numbers with Gaussian Mersenne Coefficients

Öz

In this paper, we consider hybrid numbers with Gaussian Mersenne coefficients and investigate their interesting properties such as the Binet formula, Cassini, Catalan, Vajda, D’Ocagne and Honsberger identities. Moreover, we illustrate the results with some examples.

Anahtar Kelimeler

• Hybrid Gaussian Mersenne
• Generating function
• Binet formula
• Cassini identity
• Catalan identity
• Vajda identity
• D’Ocagne identity
• Honsberger identity

Kaynakça

1. [1] M. Ozdemir, Introduction to Hybrid Numbers. Adv. Appl. Clifford Algebras, (2018), 28:11
2. [2] D. Tascı, (2021), On Gaussian Mersenne Numbers, Journal of Science and Arts,21,s1021-1028, DOI:10.46939/j.sci.arts-21.4-a13
3. [3] E. Ozkan, M. Uysal, (2021), Mersenne-Lucas Hybrid Numbers, Mathematica Montisnigri 52:17-29, DOI: 10.20948/mathmontis-2021-52-2
4. [4] D. Ta ̧scı, E. Sevgi, Some Properties between Mersenne, Jacobsthal and Jacobsthal-Lucas Hybrid Numbers, Chaos, Solitons and Fractals, 146, 110862, (2021).
5. [5] Y. Soykan, E. Ta ̧sdemir, 2021, Generalized Tetranacci Hybrid Numbers, Annales Mathematicae Silesianae,35(113-130), DOI:10.2478/amsil-2020-0021
6. [6] Y. Alp, EG. Kocer, 2021, Hybrid Leonardo numbers,Science Direct, DOI:10.1016/j.chaos.2021.111128
7. [7] Z. Isbilir, N. Gurses, 2021, Pentanacci and Pentanacci-Lucas hybrid numbers, Journal of Discrete Mathematical Sciences and Cryptography, DOI:10.1080/09720529.2021.1936899
8. [8] EG. Kocer, H. Alsan, 2021, Generalized Hybrid Fibonacci and Lucas p-numbers, Indian Journal of pure and Applied Mathematics, DOI:10.1007/s13226-021-00201-w

9. [9] C. Kızılates , A new generalization of Fibonacci hybrid and Lucas hybrid numbers, Chaos,Solitons and Fractals, 130, (2020).
10. [10] A.Szynal-Liana, The Horadam hybrid numbers, Discussiones Mathematicae–General Algebra and Applications, 38, (2018)
11. [11] H. M. Srivastava and H. L. Manocha, A Treatise on Generating Functions, Halsted Press (Ellis Horwood Limited, Chichester), John Wiley and Sons, New York, 1984.
12. [12] M. Uysal, E. Ozkan, Padovan Hybrid Quaternions and Some Properties, Journal of Science and Arts, Volume 22, Issue 1, pp. 121-132, 2022.
13. [13] A. Szynal-Liana, I. Wloch, On generalized Mersenne hybrid numbers, Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica, Vol 74, No 1, 2020