A356580 - OEIS

A356580

Decimal expansion of log(2) - gamma - 1/2 (negated).

3, 8, 4, 0, 6, 8, 4, 8, 4, 3, 4, 1, 5, 8, 7, 5, 5, 1, 1, 8, 9, 2, 7, 9, 9, 6, 8, 6, 2, 4, 2, 2, 5, 8, 6, 2, 9, 6, 6, 6, 5, 9, 2, 0, 1, 5, 7, 9, 6, 6, 8, 3, 4, 4, 6, 8, 5, 0, 8, 7, 2, 2, 5, 3, 9, 1, 4, 7, 4, 1, 0, 4, 8, 0, 7, 9, 6, 9, 9, 5, 5, 3, 3, 1, 0, 8, 3, 7, 3, 6, 2, 9, 5, 3, 2, 8, 0, 6, 1, 9, 7, 2, 6, 2, 9

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OFFSET

0,1

COMMENTS

Called the Lugo constant after Isabel Lugo.

REFERENCES

HyonChol Kim, WiSong Han, and JunHyok So, Recent Advances in the Approximation of Constants and Special Function, Scholars' Press, 2021, p. 62.

LINKS

Table of n, a(n) for n=0..104.

Chao-Ping Chen, Inequalities for the Lugo and Euler-Mascheroni constants, Applied Mathematics Letters, Vol. 25, No. 5 (2012), pp. 787-792.

Chao-Ping Chen and H. M. Srivastava, New representations for the Lugo and Euler-Mascheroni constants, Applied Mathematics Letters, Vol. 24, No. 7 (2011), pp. 1239-1244.

Chao-Ping Chen and H. M. Srivastava, New representations for the Lugo and Euler-Mascheroni constants. II, Applied Mathematics Letters, Vol. 25, No. 3 (2012), pp. 333-338.

Isabel Lugo, Math 114: An Euler-Maclaurin summation, 2007. [Wayback Machine copy]

Nikos Mantzakouras and Carlos López, New Formulas for the Euler-Mascheroni Constant and other Consequences derived from the Acceptance of Hyperbolicity of Jensen Polynomials and the Analysis of the Turán Moments for the xi-Function, arXiv preprint, arXiv:2112.11228 [math.GM], 2021; HAL link.

FORMULA

Equals lim_{n->oo} Sum{i,j=1..n} 1/(i+j) - (2*log(2))*n + log(n) (Lugo, 2007).

EXAMPLE

-0.38406848434158755118927996862422586296665920157966...

MATHEMATICA

RealDigits[Log[2] - EulerGamma - 1/2, 10, 100][[1]]

PROG

(PARI) log(2) - Euler - 1/2

CROSSREFS

Cf. A001620 (gamma), A002162, A356581.