On unrestricted dual-generalized complex Horadam numbers

Year 2024, Volume: 73 Issue: 2, 517 - 528, 21.06.2024

Nacima Rosa Ait-amrane , Elif Tan

https://doi.org/10.31801/cfsuasmas.1406328

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

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