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Mathematics 2017, 5(1), 13; doi:10.3390/math5010013

A Few Finite Trigonometric Sums

1
Institute of Physics, Sachivalaya Marg, Bhubaneswar 751005, India
2
Homi Bhabha National Institute, Training School Complex, Anushakti Nagar, Mumbai 400085, India
*
Author to whom correspondence should be addressed.
Academic Editor: Palle E.T. Jorgensen
Received: 30 November 2016 / Revised: 3 February 2017 / Accepted: 13 February 2017 / Published: 18 February 2017
View Full-Text   |   Download PDF [381 KB, uploaded 18 February 2017]

Abstract

Finite trigonometric sums occur in various branches of physics, mathematics, and their applications. These sums may contain various powers of one or more trigonometric functions. Sums with one trigonometric function are known; however, sums with products of trigonometric functions can become complicated, and may not have a simple expression in a number of cases. Some of these sums have interesting properties, and can have amazingly simple values. However, only some of them are available in the literature. We obtain a number of such sums using the method of residues. View Full-Text
Keywords: series sum; complex variables; residue theorem series sum; complex variables; residue theorem
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Datta, C.; Agrawal, P. A Few Finite Trigonometric Sums. Mathematics 2017, 5, 13.

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