One-parameter generalization of Jacobsthal elliptic quaternions
Dorota BRÓD, Anetta SZYNAL-LIANA
Received May 2, 2025. Published online January 9, 2026.
Abstract: We introduce and study Jacobsthal elliptic quaternions and their one-parameter generalization. We present some fundamental properties of them and several identities involving these numbers, among others the Binet-type formula, the Catalan, Cassini, d'Ocagne, and Vajda identities. Moreover, we give the generating functions and matrix generators for these numbers.
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Affiliations: Dorota Bród (corresponding author), Anetta Szynal-Liana, Rzeszow University of Technology, The Faculty of Mathematics and Applied Physics, al. Powstańców Warszawy 12, 35-029 Rzeszów, Poland, e-mail: dorotab@prz.edu.pl, aszynal@prz.edu.pl
