Summation formulae for finite cotangent sums
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.
Кључне речи:Trigonometric sums / Finite summation / Cotangent sums / Alternate cotangent sums / Contour integration / Cauchy residue theorem / Higher order Bernoulli polynomials / Bernoulli polynomials / Bernoulli numbers
Извор:Applied Mathematics and Computation, 2009, 215, 3, 1135-1140
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