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de Bruijn Constant

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The de Bruijn constant, also called the Copson-de Bruijn constant, is the minimal constant

c=1.1064957714...

(OEIS A113276) such that the inequality

sum_(n=1)^inftya_n<=csum_(n=1)^inftysqrt((a_n^2+a_(n+1)^2+a_(n+2)^2+...)/n)

always holds.

See also

de Bruijn-Newman Constant

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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. R. 'Copson-de Bruijn Constant." §3.5 in Mathematical Constants. Cambridge, England: Cambridge University Press, pp. 217-219, 2003.Sloane, N. J. A. Sequence A113276 in "The On-Line Encyclopedia of Integer Sequences."

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de Bruijn Constant

Cite this as:

Weisstein, Eric W. "de Bruijn Constant." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/deBruijnConstant.html

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