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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.

Finch, S. ``Favorite Mathematical Constants.'' http://www.mathsoft.com/asolve/constant/copson/copson.html




© 1996-9 Eric W. Weisstein
1999-05-24