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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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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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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DOI: https://doi.org/10.1007/978-981-99-0447-1_23
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