Euler's constant: Euler's work and modern developments

@article{Lagarias2013EulersCE,
  title={Euler's constant: Euler's work and modern developments},
  author={Jeffrey C. Lagarias},
  journal={Bulletin of the American Mathematical Society},
  year={2013},
  volume={50},
  pages={527-628}
}
  • J. Lagarias
  • Published 7 March 2013
  • Mathematics
  • Bulletin of the American Mathematical Society
This paper has two parts. The first part surveys Euler's work on the constant gamma=0.57721... bearing his name, together with some of his related work on the gamma function, values of the zeta function and divergent series. The second part describes various mathematical developments involving Euler's constant, as well as another constant, the Euler-Gompertz constant. These developments include connections with arithmetic functions and the Riemann hypothesis, and with sieve methods, random… 

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