The evaluation of Tornheim double sums. Part 2

By Olivier Espinosa, Victor H. Moll. 2005

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AbstractWe 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 $$\int_{0}^{1}\log\Gamma(q)B_{k}(q)\operatorname{Cl}_{l+1}(2\pi q)\,dq,\vspace*{-3pt}$$ with k+l=N, where Bk(q) is a Bernoulli polynomial and Cl l+1(x) is a Clausen function.

Subfields: Algebra and Number Theory, Applied Mathematics

View Paper: https://www.semanticscholar.org/paper/058aabdd56a837f4751c0c7afe4eb7000abdacc1

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In Algebra and Number Theory

  1. Jonathan Michael Borwein
  2. David M. Bradley
  3. Li Guo
  4. J. Okuda
  5. K. Ihara
  6. Kurusch Ebrahimi-Fard
  7. Michael E. Hoffman
  8. Jianqiang Zhao

In Applied Mathematics

  1. David M. Bradley
  2. Jonathan Michael Borwein

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