Affiliation:
1. Department of Computer Engineering, Faculty of Engineering and Architecture, Istanbul Gelisim University, Istanbul, Türkiye
Abstract
In this investigation, the aim is to determine a generalized quaternionic
sequence with Vietoris' number components depending on 2-parameters ? and ?.
Considering specific real values ? and ?, various types of classical
quaternionic sequence with Vietoris' number components can be obtained as
real, split, split-semi and so on. The fundamental algebraic structures,
several classical expressions, a two and three term recurrence relations are
identified, as well as Catalan-like, generating function and Binet-like
formulas. Furthermore, a determinantal approach is used to generate the
generalized quaternionic sequence with Vietoris' number components.
Publisher
National Library of Serbia
Reference33 articles.
1. B. Bajorska-Harapińska, B. Smolén, R. Wituła, On quaternion equivalents for quasi-Fibonacci numbers, shortly quaternaccis, Adv. Appl. Clifford Algebr. 29 (2019), 1-27. https://doi.org/10.1007/s00006-019-0969-9
2. I. Cação, M. I. Falcão, H. R. Malonek, Hypercomplex polynomials, Vietoris' rational numbers and a related integer numbers sequence, Complex Anal. Oper. Theory 11 (2017), 1059-1076. http://dx.doi.org/10.1007/s11785-017-0649-5
3. I. Cação, M. I. Falcão, H. R. Malonek, On Vietoris' number sequence and combinatorial identities with quaternions, 2017. Available from: https://core.ac.uk/download/pdf/132797994.pdf
4. I. Cação, M. I. Falcão, H. R. Malonek, Combinatorial identities in the context of hypercomplex function theory, In AIP Conference Proceedings, AIP Publishing LLC, 1978 (2018), 280004. https://doi.org/10.1063/1.5043904
5. I. Cação, M. I. Falcão, H. R. Malonek, On generalized Vietoris' number sequences, Discrete Appl. Math. 269 (2019), 77-85. https://doi.org/10.1016/j.dam.2018.10.017