Summation formulae for finite cotangent sums

Cvijović, Đurđe

doi:10.1016/j.amc.2009.06.053

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2009

Authors

Cvijović, Đurđe

Article (Published version)

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Abstract

Recently, a half-dozen remarkably general families of the finite trigonometric sums were summed in closed-form by choosing a particularly convenient integration contour and making use of the calculus of residues. In this sequel, we show that this procedure can be further extended and we find the summation formulae, in terms of the higher order Bernoulli polynomials and the ordinary Bernoulli polynomials, for four general families of the finite cotangent sums. (C) 2009 Elsevier Inc. All rights reserved.

Keywords:

Trigonometric sums / Finite summation / Cotangent sums / Alternate cotangent sums / Contour integration / Cauchy residue theorem / Higher order Bernoulli polynomials / Bernoulli polynomials / Bernoulli numbers

Source:
Applied Mathematics and Computation, 2009, 215, 3, 1135-1140

Funding / projects:

Fizička hemija dinamičkih stanja i struktura neravnotežnih sistema - od monotone do oscilatorne evolucije i haosa (RS-MESTD-MPN2006-2010-142025)
Ortogonalni sistemi i primene (RS-MESTD-MPN2006-2010-144004)

DOI: 10.1016/j.amc.2009.06.053

ISSN: 0096-3003

WoS: 000269403200028

Scopus: 2-s2.0-69249218974

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TY  - JOUR
AU  - Cvijović, Đurđe
PY  - 2009
UR  - https://vinar.vin.bg.ac.rs/handle/123456789/3778
AB  - Recently, a half-dozen remarkably general families of the finite trigonometric sums were summed in closed-form by choosing a particularly convenient integration contour and making use of the calculus of residues. In this sequel, we show that this procedure can be further extended and we find the summation formulae, in terms of the higher order Bernoulli polynomials and the ordinary Bernoulli polynomials, for four general families of the finite cotangent sums. (C) 2009 Elsevier Inc. All rights reserved.
T2  - Applied Mathematics and Computation
T1  - Summation formulae for finite cotangent sums
VL  - 215
IS  - 3
SP  - 1135
EP  - 1140
DO  - 10.1016/j.amc.2009.06.053
ER  -

@article{
author = "Cvijović, Đurđe",
year = "2009",
abstract = "Recently, a half-dozen remarkably general families of the finite trigonometric sums were summed in closed-form by choosing a particularly convenient integration contour and making use of the calculus of residues. In this sequel, we show that this procedure can be further extended and we find the summation formulae, in terms of the higher order Bernoulli polynomials and the ordinary Bernoulli polynomials, for four general families of the finite cotangent sums. (C) 2009 Elsevier Inc. All rights reserved.",
journal = "Applied Mathematics and Computation",
title = "Summation formulae for finite cotangent sums",
volume = "215",
number = "3",
pages = "1135-1140",
doi = "10.1016/j.amc.2009.06.053"
}

Cvijović, Đ.. (2009). Summation formulae for finite cotangent sums. in Applied Mathematics and Computation, 215(3), 1135-1140.
https://doi.org/10.1016/j.amc.2009.06.053

Cvijović Đ. Summation formulae for finite cotangent sums. in Applied Mathematics and Computation. 2009;215(3):1135-1140.
doi:10.1016/j.amc.2009.06.053 .

Cvijović, Đurđe, "Summation formulae for finite cotangent sums" in Applied Mathematics and Computation, 215, no. 3 (2009):1135-1140,
https://doi.org/10.1016/j.amc.2009.06.053 . .