The evaluation of Tornheim double sums. Part 2

作者：Espinosa Olivier^*; Moll Victor H

来源：Ramanujan Journal, 2010, 22(1): 55-99.

DOI：10.1007/s11139-009-9181-1

• Hurwitz zeta function
• Tornheim sum
• Witten zeta function

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
integral(1)(0) log Gamma(q)B(k)(q)Cl(l+1)(2 pi q)dq,
with k + l = N, where B(k)(q) is a Bernoulli polynomial and Cl(l+1)(x) is a Clausen function.

• 出版日期2010-5