Rediscovery of Malmsten’s integrals, their evaluation by contour integration methods and some related results

@article{Blagouchine2014RediscoveryOM,
  title={Rediscovery of Malmsten’s integrals, their evaluation by contour integration methods and some related results},
  author={Iaroslav V. Blagouchine},
  journal={The Ramanujan Journal},
  year={2014},
  volume={35},
  pages={21-110}
}
This article is devoted to a family of logarithmic integrals recently treated in mathematical literature, as well as to some closely related results. First, it is shown that the problem is much older than usually reported. In particular, the so-called Vardi’s integral, which is a particular case of the considered family of integrals, was first evaluated by Carl Malmsten and colleagues in 1842. Then, it is shown that under some conditions, the contour integration method may be successfully used… 

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