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A265162 Decimal expansion of Sum_{k>=1} (-1)^k*log(k)/sqrt(k). 3
1, 9, 3, 2, 8, 8, 8, 3, 1, 6, 3, 9, 2, 8, 2, 7, 3, 8, 9, 6, 4, 6, 1, 5, 4, 5, 9, 3, 5, 5, 2, 3, 8, 1, 1, 4, 2, 9, 5, 2, 7, 0, 2, 2, 2, 5, 2, 9, 2, 2, 1, 9, 9, 2, 2, 9, 3, 6, 0, 4, 8, 1, 0, 3, 3, 4, 4, 0, 1, 6, 6, 6, 4, 4, 4, 4, 6, 8, 9, 8, 7, 3, 4, 9, 8, 6, 8, 0, 9, 2, 0, 8, 7, 7, 7, 8, 1, 6, 3, 6, 8, 4, 5, 7, 2, 6 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..10000

FORMULA

Equals ((3-sqrt(2))*log(2)/2 - (sqrt(2)-1)*(2*gamma + Pi + 2*log(Pi))/4) * Zeta(1/2), where gamma is the Euler-Mascheroni constant A001620.

A265162/A113024 = gamma/2 + Pi/4 - (1/2 + sqrt(2))*log(2) + log(Pi)/2.

EXAMPLE

0.1932888316392827389646154593552381142952702225292219922936048103344...

MAPLE

evalf(sum((-1)^k*log(k)/sqrt(k), k=1..infinity), 120);

MATHEMATICA

RealDigits[((3-Sqrt[2])*Log[2]/2 - (Sqrt[2]-1)*(2*EulerGamma + Pi + 2*Log[Pi])/4) * Zeta[1/2], 10, 106][[1]]

PROG

(PARI) ((3-sqrt(2))*log(2)/2 - (sqrt(2)-1)*(2*Euler + Pi + 2*log(Pi))/4)* zeta(1/2) \\ G. C. Greubel, Apr 15 2018

CROSSREFS

Cf. A091812, A113024.

Sequence in context: A010538 A216102 A019721 * A259837 A215189 A201320

Adjacent sequences:  A265159 A265160 A265161 * A265163 A265164 A265165

KEYWORD

nonn,cons

AUTHOR

Vaclav Kotesovec, Dec 03 2015

STATUS

approved

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Last modified January 20 14:40 EST 2019. Contains 319333 sequences. (Running on oeis4.)