de Bruijn Constant

Also called the Copson-de Bruijn Constant. It is defined by

$\begin{displaymath} \sum_{n=1}^\infty a_n\leq c \sum_{n=1}^\infty \sqrt{{a_n}^2+{a_{n+1}}^2+{a_{n+2}}^2+\ldots\over n}\,. \end{displaymath}$

where

$\begin{displaymath} c=1.0164957714\ldots. \end{displaymath}$

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.