Closed-form summation of two families of finite tangent sums
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.
Кључне речи:tangent sums / finite summation / contour integration / cauchy residue theorem / Bernoulli polynomials / Euler polynomials / higher order Bernoulli polynomials
Извор:Applied Mathematics and Computation, 2008, 196, 2, 661-665
ISSN: 0096-3003 (print)