Also called the Copson-de Bruijn Constant. It is defined by
References
Copson, E. T. ``Note on Series of Positive Terms.'' J. London Math. Soc. 2, 9-12, 1927.
Copson, E. T. ``Note on Series of Positive Terms.'' J. London Math. Soc. 3, 49-51, 1928.
de Bruijn, N. G. Asymptotic Methods in Analysis. New York: Dover, 1981.
Finch, S. ``Favorite Mathematical Constants.'' http://www.mathsoft.com/asolve/constant/copson/copson.html