On unrestricted dual-generalized complex Horadam numbers

Authors : Nacima Rosa Ait-amrane, Elif Tan

Pages : 517-528

Doi:10.31801/cfsuasmas.1406328

View : 37 | Download : 130

Publication Date : 2024-06-21

Article Type : Research Paper

Abstract :This research introduces a novel category of dual-generalized complex numbers, with components represented by unrestricted Horadam numbers. We present various recurrence relations, summation formulas, the Binet formula, and the generating function associated with these numbers. Additionally, a comprehensive bilinear index-reduction formula is derived, which encompasses Vajda’s, Catalan’s, Cassini’s, D’Ocagne’s, and Halton’s identities as specific cases.
Keywords : Hypercomplex numbers, dual generalized complex numbers, Horadam numbers, Fibonacci numbers