Open AccessOn split r-Jacobsthal quaternions
Author(s) -
Dorota Bród
Publication year - 2020
Publication title -
annales universitatis mariae curie-skłodowska. sectio a, mathematica
Language(s) - English
Resource type - Journals
eISSN - 2083-7402
pISSN - 0365-1029
DOI - 10.17951/a.2020.74.1.1-14
Subject(s) - quaternion , generalization , identity (music) , mathematics , convolution (computer science) , catalan number , algebra over a field , combinatorics , pure mathematics , computer science , mathematical analysis , geometry , artificial intelligence , physics , artificial neural network , acoustics
In this paper we introduce a one-parameter generalization of the split Jacobsthal quaternions, namely the split r-Jacobsthal quaternions. We give a generating function, Binet formula for these numbers. Moreover, we obtain some identities, among others Catalan, Cassini identities and convolution identity for the split r-Jacobsthal quaternions.