Tan, ElifYilmaz, SemihSahin, Murat2020-06-252020-06-252016closedAccess0960-07791873-2887https://doi.org/10.1016/j.chaos.2016.01.025https://hdl.handle.net/20.500.12587/6601Motivated by the our recent work in Tan et al., 2016, related to the bi-periodic Fibonacci quaternions, here we introduce the bi-periodic Lucas quaternions that gives the Lucas quaternions as a special case. We give the generating function and the Binet formula for these quaternions. Also, we give the relationships between bi-periodic Fibonacci quaternions and bi-periodic Lucas quaternions. (C) 2016 Elsevier Ltd. All rights reserved.eninfo:eu-repo/semantics/closedAccessLucas sequenceGeneralized Lucas sequenceRecurrence relationsQuaternionsArticle8513814210.1016/j.chaos.2016.01.0252-s2.0-84958966029Q1WOS:000371921500016Q2