545
Views
0
CrossRef citations to date
0
Altmetric
Notes

An Elementary Derivation of Finite Cotangent Sums

Pages 775-780 | Received 10 Feb 2021, Accepted 23 Jul 2021, Published online: 14 Jul 2022

References

  • Annaby, M. H., Asharabi, R. M. (2011). Exact evaluations of finite trigonometric sums by sampling theorems. Acta Math. Sci. Ser. B (Engl. Ed.). 31(2): 408–418.
  • Apostol, T. M. (1973). Another elementary proof of Euler’s formula for ζ(2n) . Amer. Math. Monthly. 80(4): 425–431.
  • Berndt, B. C., Yeap, B. P. (2002). Explicit evaluations and reciprocity theorems for finite trigonometric sums. Adv. Appl. Math. 29(3): 358–385.
  • Chu, W., Marini, A. (1999). Partial fractions and trigonometric identities. Adv. Appl. Math. 23: 115–175.
  • Cvijović, D. (2009). Summation formulae for finite cotangent sums. Appl. Math. Comput. 215(3): 1135–1140.
  • Cvijović, D., Klinowski, J. (2000). Finite cotangent sums and the Riemann zeta function. Math. Slovaca. 50(2): 149–157.
  • Cvijović, D., Klinowski, J., Srivastava, H. M. (2003). Some polynomials associated with Williams’ limit formula for ζ(2n) . Math. Proc. Cambridge Philos. Soc. 135(2): 199–209.
  • Ejsmont, W., Lehner, F. (2020). The trace method for cotangent sums. J. Comb. Theory. Ser. A. 177: Article 105324. DOI: 10.1016/j.jcta.2020.105324.
  • Gessel, I. M. (1997). Generating functions and generalized Dedekind sums. Electron. J. Comb. 4(2): Research Paper 11.
  • Papadimitriou, I. (1973). A simple proof of the formula ∑k=1∞k−2=π2/6 . Amer. Math. Monthly. 80(4): 424–425.
  • Williams, K. S., Zhang, N. Y. (1994). Evaluation of two trigonometric sums. Math. Slovaca. 44(5): 575–583.
  • Yuan, H. (2020). Explicit expressions for finite trigonometric sums. J. Math. Anal. Appl. 484(1): Article 123702.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.