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Generalized Cassini identities via the generalized Fibonacci fundamental system. Applications

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Abstract

In this paper we explore the generalized Cassini identities for the weighted generalized Fibonacci sequences, through the associated generalized Fibonacci fundamental system. Some algebraic, combinatoric and analytic properties of these identities are established. Applications to generalized Fibonacci and Pell numbers are provided, and some special cases are studied.

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Acknowledgements

The authors express their sincere thanks to the Universidade Federal da Grande Dourados-UFGD/FACET/MEC - Brazil and to the Universidade Federal de Mato Grosso do Sul - UFMS/MEC - Brazil for their valuable support. The third author is supported by the Profmat and PPGEdumat programs of the INMA-UFMS. He expresses his sincere thanks to the INMA and the UFMS for their valuable support and encouragements.

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Authors and Affiliations

  1. Mathematics Department - UFGD, Dourados, MS, Brazil

    I. M. Craveiro

  2. Institute of Mathematics, INMA - UFMS, Campo Grande, MS, Brazil

    E. V. Pereira Spreafico & M. Rachidi

Authors
  1. I. M. Craveiro
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  2. E. V. Pereira Spreafico
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  3. M. Rachidi
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Correspondence to E. V. Pereira Spreafico.

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Communicated by Sanoli Gun.

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Craveiro, I.M., Pereira Spreafico, E.V. & Rachidi, M. Generalized Cassini identities via the generalized Fibonacci fundamental system. Applications. Indian J Pure Appl Math (2023). https://doi.org/10.1007/s13226-023-00430-1

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