Closed-form summation of two families of finite tangent sums
Apstrakt
In our recent paper with Srivastava [D. Cvijovic, H.M. Srivastava, Summation of a family of finite secant sums, Appl. Math. Comput. 190 (2007) 590-598] a remarkably general family of the finite secant sums was 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 extended and we find the summation formulae in terms of the higher order Bernoulli polynomials and the ordinary Bernoulli and Enter polynomials for two general families of the finite tangent sums. (C) 2007 Elsevier Inc. All rights reserved.
Ključne reči:
tangent sums / finite summation / contour integration / cauchy residue theorem / Bernoulli polynomials / Euler polynomials / higher order Bernoulli polynomialsIzvor:
Applied Mathematics and Computation, 2008, 196, 2, 661-665
DOI: 10.1016/j.amc.2007.07.001
ISSN: 0096-3003
WoS: 000253631700018
Scopus: 2-s2.0-38849176256
Kolekcije
Institucija/grupa
VinčaTY - JOUR AU - Cvijović, Đurđe PY - 2008 UR - https://vinar.vin.bg.ac.rs/handle/123456789/3371 AB - In our recent paper with Srivastava [D. Cvijovic, H.M. Srivastava, Summation of a family of finite secant sums, Appl. Math. Comput. 190 (2007) 590-598] a remarkably general family of the finite secant sums was 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 extended and we find the summation formulae in terms of the higher order Bernoulli polynomials and the ordinary Bernoulli and Enter polynomials for two general families of the finite tangent sums. (C) 2007 Elsevier Inc. All rights reserved. T2 - Applied Mathematics and Computation T1 - Closed-form summation of two families of finite tangent sums VL - 196 IS - 2 SP - 661 EP - 665 DO - 10.1016/j.amc.2007.07.001 ER -
@article{ author = "Cvijović, Đurđe", year = "2008", abstract = "In our recent paper with Srivastava [D. Cvijovic, H.M. Srivastava, Summation of a family of finite secant sums, Appl. Math. Comput. 190 (2007) 590-598] a remarkably general family of the finite secant sums was 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 extended and we find the summation formulae in terms of the higher order Bernoulli polynomials and the ordinary Bernoulli and Enter polynomials for two general families of the finite tangent sums. (C) 2007 Elsevier Inc. All rights reserved.", journal = "Applied Mathematics and Computation", title = "Closed-form summation of two families of finite tangent sums", volume = "196", number = "2", pages = "661-665", doi = "10.1016/j.amc.2007.07.001" }
Cvijović, Đ.. (2008). Closed-form summation of two families of finite tangent sums. in Applied Mathematics and Computation, 196(2), 661-665. https://doi.org/10.1016/j.amc.2007.07.001
Cvijović Đ. Closed-form summation of two families of finite tangent sums. in Applied Mathematics and Computation. 2008;196(2):661-665. doi:10.1016/j.amc.2007.07.001 .
Cvijović, Đurđe, "Closed-form summation of two families of finite tangent sums" in Applied Mathematics and Computation, 196, no. 2 (2008):661-665, https://doi.org/10.1016/j.amc.2007.07.001 . .