The Evaluation of Tornheim Double Sums
نویسنده
چکیده
We provide an explicit formula for the Tornheim double series in terms of integrals involving the Hurwitz zeta function. We also study the limit when the parameters of the Tornheim sum become natural numbers, and show that in that case it can be expressed in terms of definite integrals of triple products of Bernoulli polynomials and the Bernoulli function Ak(q) := kζ(1− k, q).
منابع مشابه
The Evaluation of Tornheim Double Sums. Part 2
We provide an explicit formula for the Tornheim double series T (a, 0, c) in terms of an integral involving the Hurwitz zeta function. For integer values of the parameters, a = m, c = n, we show that in the most interesting case of even weight N := m + n the Tornheim sum T (m, 0, n) can be expressed in terms of zeta values and the family of integrals
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We provide an explicit formula for the Tornheim double series T (a, 0, c) in terms of an integral involving the Hurwitz zeta function. For integer values of the parameters, a = m, c = n, we show that in the most interesting case of even weight N := m + n the Tornheim sum T (m, 0, n) can be expressed in terms of zeta values and the family of integrals
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