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Search: id:A130705
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| A130705 |
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Floors of constants in De Bruijn's approach to weighted Carleman's inequality. |
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+0
1
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| -109, -42, -26, -18, -14, -12, -10, -9, -8, -7, -6, -6, -5, -5, -5, -4, -4, -4, -4, -4, -3, -3, -3, -3, -3, -3, -3, -3, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -1
(list; graph; listen)
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OFFSET
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2,1
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COMMENT
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From Gao's abstract: "We study finite sections of weighted Carleman's inequality following the approach of De Bruijn. Similar to the unweighted case, we obtain an asymptotic expression for the optimal constant."
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REFERENCES
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N. G. De Bruijn, Carleman's inequality for finite series, Nederl. Akad. Wetensch. Proc. Ser. A 66 = Indag, pp. 505-514.
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LINKS
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Peng Gao, Finite Sections of Weighted Carleman's Inequality, arXiv:0707.0077
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FORMULA
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a(n) = floor(e - (2*(pi^2)*e)/((log(n))^2)).
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EXAMPLE
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a(2) = -109 because e - (2*(pi^2)*e)/((log(2))^2) ~ -108.9611770171388392925257212314455433803548032218666994709.
a(3) = -42 because e - (2*(pi^2)*e)/((log(3))^2) ~ -41.7382232411477828847325690963577817095329948893743754723.
a(4) = -26 because e - (2*(pi^2)*e)/((log(4))^2) ~ -25.20158288294042589661121470434688897177076548519170518650.
a(30) = -2 because e - (2*(pi^2)*e)/((log(30))^2) ~ -1.92003649778404604739381818236913112747520.
a(45) = -1 because e - (2*(pi^2)*e)/((log(45))^2) ~ -0.98456269963010489451493724472555817336322761419762175593.
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CROSSREFS
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Sequence in context: A033535 A077728 A093724 this_sequence A051046 A159027 A039492
Adjacent sequences: A130702 A130703 A130704 this_sequence A130706 A130707 A130708
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KEYWORD
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easy,sign,new
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AUTHOR
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Jonathan Vos Post (jvospost3(AT)gmail.com), Jul 03 2007
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EXTENSIONS
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Replaced arxiv URL by non-cached version - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 30 2009
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