# 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…
131 Citations
Fractional parts and their relations to the values of the Riemann zeta function
A well-known result, due to Dirichlet and later generalized by de la Vallée–Poussin, expresses a relationship between the sum of fractional parts and the Euler–Mascheroni constant. In this paper, we
On certain alternating series involving zeta and multiple zeta values
In this article, we consider various generalizations of Euler's famous relation $\gamma = \sum_{n\geq 2} (-1)^n \frac{\zeta(n)}{n}$ linking Euler's constant $\gamma$ to special values of the
Euler's factorial series, Hardy integral, and continued fractions
• Mathematics
• 2021
. We study p -adic Euler’s series E p ( t ) = P ∞ k =0 k ! t k at a point p a , a ∈ Z ≥ 1 , and use Pad´e approximations to prove a lower bound for the p -adic absolute value of the expression cE p (
ON A GENERALIZATION OF EULER’S CONSTANT
A one parameter generalization of Euler’s constant γ from [Numer. Algorithms 46(2) (2007) 141–151] is investigated, and additional expressions for γ are derived. Included are forms involving the
Another Alternating Analogue of Euler’s Constant
Abstract In 2005 Jonathan Sondow found several interesting analogies between Euler’s constant γ and revealing that the latter may be regarded as the alternating analogue of Euler’s constant. In this
From Euler's play with infinite series to the anomalous magnetic moment
During a first St. Petersburg period Leonhard Euler, in his early twenties, became interested in the Basel problem: summing the series of inverse squares (posed by Pietro Mengoli in mid 17th
Euler ’ s Constant : New Insights by Means of Minus One Factorial
The great object of this paper is to furnish, in a concise and plain manner, new insights into that mysterious constant whose arithmetic nature was shrouded in obscurity for over 250 years, the