Secant and Cosecant Sums and Bernoulli-nörlund Polynomials
نویسنده
چکیده
We give explicit formulae for sums of even powers of secant and cosecant values in terms of Bernoulli numbers and central factorial numbers.
منابع مشابه
Summation of a family of finite secant sums
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. 2007 Elsevier Inc. All rig...
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Abstract. We show that the classical Faulhaber’s theorem on sums of odd powers also holds for an arbitrary arithmetic progression, namely, the odd power sums of any arithmetic progression a + b, a + 2b, . . . , a + nb is a polynomial in na+ n(n+ 1)b/2. The coefficients of these polynomials are given in terms of the Bernoulli polynomials. Following Knuth’s approach by using the central factorial...
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تاریخ انتشار 2008