Construction of dual-generalized complex Fibonacci and Lucas quaternions - Senturk, G. Y.; Gurses, N.; Yuce, S. (VASYL STEFANYK PRECARPATHIAN NATL UNIV, 2022)
The aim of this paper is to construct dual-generalized complex Fibonacci and Lucas quaternions. It examines the properties both as dual-generalized complex number and as quaternion. Addi-tionally, general recurrence relations, Binet's formulas, Tagiuri's (or Vajda's like), Honsberger's, d'Ocagne's, Cassini's and Catalan's identities are obtained. A series of matrix representations of these special quaternions is introduced. Finally, the multiplication of dual-generalized complex Fi-bonacci and Lucas quaternions are also expressed as their different matrix representations.
Keywords: quaternion; dual-generalized complex number; Fibonacci number; Lucas number; NUMBERS; Mathematics