Evaluation of some reciprocal trigonometric sums via partial fraction decomposition


ARIKAN T., Prodinger H.

KUWAIT JOURNAL OF SCIENCE, vol.47, no.1, pp.14-21, 2020 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 47 Issue: 1
  • Publication Date: 2020
  • Journal Name: KUWAIT JOURNAL OF SCIENCE
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Arab World Research Source, zbMATH
  • Page Numbers: pp.14-21
  • Hacettepe University Affiliated: Yes

Abstract

Recently, Melham computed some finite sums in which the denominator of the summand includes products of 'sine' or 'cosine'. In this paper, generalizations of the sums, which he studied in 2016, are presented, by allowing arbitrary factors in the denominator of the summand. Our approach uses the elementary technique of partial fraction decomposition. Furthermore, some of the sums, which he studied in 2017, are treated in the same style.