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THE EVALUATION OF TORNHEIM DOUBLE SUMS. PART 2
"... Abstract. 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 e ..."
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Abstract. 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 Z 1 logΓ(q)Bk(q)Cll+1(2πq) dq, 0 with k + l = N, where Bk(q) is a Bernoulli polynomial and Cll+1(x) is a Clausen function. The function