Summation of a family of finite secant sums
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We use contour integrals and the Cauchy residue theorem in order to derive several summation formulas, in terms of the higher-order Bernoulli polynomials and the ordinary Bernoulli and Euler polynomials, for a remarkably general family of secant sums. Numerous (known or new) special cases are shown to follow readily from the summation formulas presented in this paper. (c) 2007 Elsevier Inc. All rights reserved.
Кључне речи:secant sums / finite summation formulas / contour integration / Cauchy residue theorem / higher-order Bernoulli polynomials / Euler polynomials and numbers
Извор:Applied Mathematics and Computation, 2007, 190, 1, 590-598
ISSN: 0096-3003 (print)