Closed-form summation of two families of finite tangent sums

Abstract

In our recent paper with Srivastava [D. Cvijović, 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 Euler polynomials for two general families of the finite tangent sums.