On unrestricted dual-generalized complex Horadam numbers

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Communications Faculty of Sciences University Ankara Series A1 Mathematics and Statistics
Volume:73 Issue:2
On unrestricted dual-generalized complex Horadam numbers

On unrestricted dual-generalized complex Horadam numbers

Authors : Nacima Rosa Aitamrane, Elif Tan

Pages : 517-528

Doi:10.31801/cfsuasmas.1406328

View : 38 | Download : 133

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

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