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Explicit Formulae of Linear Recurrences

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Mathematics and Computation (IACMC 2022)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 418))

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Abstract

One important and widely studied problem in the theory of linear recurrences is to find explicit formulae for the general term of the sequences. Having an explicit formula facilitates the research of the properties of the sequence we investigate. The main tool is to apply the fundamental theorem of homogeneous linear recurrences, but other approaches may work as well. In the present paper, we concentrate on a specific case when the characteristic polynomial of the sequence has a double zero, and on a general formula.

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References

  1. Açikel, A., Irmak, N., Szalay, L.: The \(k\)-generalized lucas numbers close to a power of 2. Math. Slovaca.

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Acknowledgements

The research was supported in part by National Research, Development and Innovation Office Grant 2019-2.1.11-TÉT-2020-00165, by Hungarian National Foundation for Scientific Research Grant No. 128088, and No. 130909, and by the Slovak Scientific Grant Agency VEGA 1/0776/21.

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Authors and Affiliations

  1. University of Sopron, Sopron, Hungary

    László Szalay

  2. J. Selye University, Komárno, Slovakia

    László Szalay

Authors
  1. László Szalay
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Correspondence to László Szalay .

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Editors and Affiliations

  1. School of Basic Sciences and Humanities, German Jordanian University, Amman, Jordan

    Dia Zeidan

  2. Department of Applied Mathematics, Universitat Politècnica de València, Valencia, Spain

    Juan C. Cortés

  3. Department of Mathematics, Zarqa University, Zarqa, Jordan

    Aliaa Burqan

  4. Department of Mathematics, Zarqa University, Zarqa, Jordan

    Ahmad Qazza

  5. MNZ, Leipzig University of Applied Sciences, Leipzig, Germany

    Jochen Merker

  6. Department of Mathematics, Zarqa University, Zarqa, Jordan

    Gharib Gharib

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© 2023 The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.

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Szalay, L. (2023). Explicit Formulae of Linear Recurrences. In: Zeidan, D., Cortés, J.C., Burqan, A., Qazza, A., Merker, J., Gharib, G. (eds) Mathematics and Computation. IACMC 2022. Springer Proceedings in Mathematics & Statistics, vol 418. Springer, Singapore. https://doi.org/10.1007/978-981-99-0447-1_23

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