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Further developments of basic trigonometric power sums

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Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas Aims and scope Submit manuscript

Abstract

In this article we present some additional and complementary remarks to an earlier paper on finite trigonometric power sums. First, we extend the results to include an offset angle in the trigonometric power in the summand. Next we include more complicated phase factors accompanying the trigonometric powers. Despite their more intricate nature, we find that these trigonometric power sums are still rational. Finally, we not only prove the conjecture raised in the earlier paper, but also generalize it.

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Authors and Affiliations

  1. School of Software, South China Normal University, Foshan, 528225, Guangdong, China

    Zhibin Du

  2. Kuwait College of Science and Technology, 13133, Doha District, Safat, Kuwait

    Carlos M. da Fonseca

  3. Chair of Computational Mathematics, University of Deusto, 48007, Bilbao, Spain

    Carlos M. da Fonseca

  4. School of Mathematics and Statistics, The University of Melbourne, Parkville, VIC, 3010, Australia

    Victor Kowalenko

Authors
  1. Zhibin Du
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  2. Carlos M. da Fonseca
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  3. Victor Kowalenko
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Correspondence to Carlos M. da Fonseca.

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Du, Z., da Fonseca, C.M. & Kowalenko, V. Further developments of basic trigonometric power sums. Rev. Real Acad. Cienc. Exactas Fis. Nat. Ser. A-Mat. 117, 112 (2023). https://doi.org/10.1007/s13398-023-01442-6

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  • DOI: https://doi.org/10.1007/s13398-023-01442-6

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