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… Expand
20 Citations
Simple evaluation of one of Malmst\'en's integrals
Three Notes on Ser's and Hasse's Representations for the Zeta-functions
Computing Stieltjes constants using complex integration
...
1
2
...

References

SHOWING 1-10 OF 56 REFERENCES
On representations and differences of Stieltjes coefficients, and other relations
A Course of Modern Analysis
Series representations for the Stieltjes constants
The Laplace transform of the digamma function: An integral due to Glasser, Manna and Oloa
Irresistible Integrals: Symbolics, Analysis and Experiments in the Evaluation of Integrals
Methods of Mathematical Physics
...
1
2
3
4
5
...