The evaluation of Tornheim double sums. Part2
2008
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
%
\int_0^1 loggamma(q) B_{k}(q) Cl_{j+1} (2 \pi q) dq,
% with k+j = N, where B_{k}(q) is a Bernoulli polynomial and \Cl_{j+1}(x) is a Clausen function.
Keywords:
- Correction
- Cite
- Save
- Machine Reading By IdeaReader
28
References
0
Citations
NaN
KQI