A new approach to Jacobsthal, Jacobsthal-Lucas numbers and dual vectors

Faik Babadağ; Faik Babadağ

doi:10.3934/math.2023946

AIMS Mathematics

2023, Volume 8, Issue 8: 18596-18606. doi: 10.3934/math.2023946

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A new approach to Jacobsthal, Jacobsthal-Lucas numbers and dual vectors

Faik Babadağ ^,

Kırıkkale University, Art & Science Faculty, Department of Mathematics, 71450, Kırıkkale, Turkey

Received: 15 February 2023 Revised: 16 May 2023 Accepted: 19 May 2023 Published: 01 June 2023
MSC : 05A15, 11B37, 11Y55

This paper gives a detailed study of a new generation of dual Jacobsthal and dual Jacobsthal-Lucas numbers using dual numbers. Also some formulas, facts and properties about these numbers are presented. In addition, a new dual vector called the dual Jacobsthal vector is presented. Some properties of this vector apply to various properties of geometry which are not generally known in the geometry of dual space. Finally, this study introduces the dual Jacobsthal and the dual Jacobsthal-Lucas numbers with coefficients of dual numbers. Some fundamental identities are demonstrated, such as the generating function, the Binet formulas, the Cassini's, Catalan's and d'Ocagne identities for these numbers.
- recurrences,
- integer sequences,
- dual number,
- dual angle,
- dual Jacobsthal numbers
Citation: Faik Babadağ. A new approach to Jacobsthal, Jacobsthal-Lucas numbers and dual vectors[J]. AIMS Mathematics, 2023, 8(8): 18596-18606. doi: 10.3934/math.2023946

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Abstract

This paper gives a detailed study of a new generation of dual Jacobsthal and dual Jacobsthal-Lucas numbers using dual numbers. Also some formulas, facts and properties about these numbers are presented. In addition, a new dual vector called the dual Jacobsthal vector is presented. Some properties of this vector apply to various properties of geometry which are not generally known in the geometry of dual space. Finally, this study introduces the dual Jacobsthal and the dual Jacobsthal-Lucas numbers with coefficients of dual numbers. Some fundamental identities are demonstrated, such as the generating function, the Binet formulas, the Cassini's, Catalan's and d'Ocagne identities for these numbers.

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