A130705 Floors of constants in de Bruijn's approach to weighted Carleman's inequality.

-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

Offset

2,1

Comments

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."

Links

Table of n, a(n) for n=2..45.

N. G. De Bruijn, Carleman's inequality for finite series, Nederl. Akad. Wetensch. Proc. Ser. A 66 = Indag, pp. 505-514.

Peng Gao, Finite Sections of Weighted Carleman's Inequality, arXiv:0707.0077 [math.CA], 2007.

Formula

a(n) = floor(e - (2*(Pi^2)*e)/((log(n))^2)).

Example

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.

Crossrefs

Sequence in context: A340348 A340347 A247440 * A253431 A253438 A263194

Adjacent sequences: A130702 A130703 A130704 * A130706 A130707 A130708

Keyword

easy,sign

Author

Jonathan Vos Post, Jul 03 2007

Status

approved