The evaluation of Tornheim double sums. Part2 - Mathematics > Number TheoryReport as inadecuate




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Abstract: We provide an explicit formula for the Tornheim double series Ta,0,c interms of an integral involving the Hurwitz zeta function. For integer values ofthe parameters, a=m, c=n, we show that in the most interesting case of evenweight N:=m+n the Tornheim sum Tm,0,n can be expressed in terms of zetavalues and the family of integrals%\int 0^1 loggammaq 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 isa Clausen function.



Author: Olivier Espinosa, Victor H. Moll

Source: https://arxiv.org/







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