Summation formulae for finite tangent and secant sums
Abstract
In a series of papers [6-10] it has been shown that nine remarkably general families of the finite trigonometric sums could be summed in closed form by making use of the calculus of residues and choosing a particularly convenient integration contour. In this sequel, new summation formulae for three general families of finite tangent and secant sums have been deduced by the same approach. (C) 2011 Elsevier Inc. All rights reserved.
Keywords:
Finite summation / Trigonometric sums / Tangent sums / Secant sums / Higher order Bernoulli polynomials / Bernoulli polynomials / Contour integration / Cauchy residue theoremSource:
Applied Mathematics and Computation, 2011, 218, 3, 741-745Funding / projects:
- Dynamics of nonlinear physicochemical and biochemical systems with modeling and predicting of their behavior under nonequilibrium conditions (RS-MESTD-Basic Research (BR or ON)-172015)
DOI: 10.1016/j.amc.2011.01.079
ISSN: 0096-3003
WoS: 000294298400020
Scopus: 2-s2.0-80052267076
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Institution/Community
VinčaTY - JOUR AU - Cvijović, Đurđe PY - 2011 UR - https://vinar.vin.bg.ac.rs/handle/123456789/4463 AB - In a series of papers [6-10] it has been shown that nine remarkably general families of the finite trigonometric sums could be summed in closed form by making use of the calculus of residues and choosing a particularly convenient integration contour. In this sequel, new summation formulae for three general families of finite tangent and secant sums have been deduced by the same approach. (C) 2011 Elsevier Inc. All rights reserved. T2 - Applied Mathematics and Computation T1 - Summation formulae for finite tangent and secant sums VL - 218 IS - 3 SP - 741 EP - 745 DO - 10.1016/j.amc.2011.01.079 ER -
@article{ author = "Cvijović, Đurđe", year = "2011", abstract = "In a series of papers [6-10] it has been shown that nine remarkably general families of the finite trigonometric sums could be summed in closed form by making use of the calculus of residues and choosing a particularly convenient integration contour. In this sequel, new summation formulae for three general families of finite tangent and secant sums have been deduced by the same approach. (C) 2011 Elsevier Inc. All rights reserved.", journal = "Applied Mathematics and Computation", title = "Summation formulae for finite tangent and secant sums", volume = "218", number = "3", pages = "741-745", doi = "10.1016/j.amc.2011.01.079" }
Cvijović, Đ.. (2011). Summation formulae for finite tangent and secant sums. in Applied Mathematics and Computation, 218(3), 741-745. https://doi.org/10.1016/j.amc.2011.01.079
Cvijović Đ. Summation formulae for finite tangent and secant sums. in Applied Mathematics and Computation. 2011;218(3):741-745. doi:10.1016/j.amc.2011.01.079 .
Cvijović, Đurđe, "Summation formulae for finite tangent and secant sums" in Applied Mathematics and Computation, 218, no. 3 (2011):741-745, https://doi.org/10.1016/j.amc.2011.01.079 . .