Double integrals and infinite products for some classical constants via analytic continuations of Lerch’s transcendent

@article{Guillera2008DoubleIA,
  title={Double integrals and infinite products for some classical constants via analytic continuations of Lerch’s transcendent},
  author={Jes{\'u}s Guillera and Jonathan Sondow},
  journal={The Ramanujan Journal},
  year={2008},
  volume={16},
  pages={247-270}
}
The two-fold aim of the paper is to unify and generalize on the one hand the double integrals of Beukers for ζ(2) and ζ(3), and of the second author for Euler’s constant γ and its alternating analog ln (4/π), and on the other hand the infinite products of the first author for e, of the second author for π, and of Ser for eγ. We obtain new double integral and infinite product representations of many classical constants, as well as a generalization to Lerch’s transcendent of Hadjicostas’s double… 
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