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A256358 Decimal expansion of log(sqrt(Pi/2)). 2
2, 2, 5, 7, 9, 1, 3, 5, 2, 6, 4, 4, 7, 2, 7, 4, 3, 2, 3, 6, 3, 0, 9, 7, 6, 1, 4, 9, 4, 7, 4, 4, 1, 0, 7, 1, 7, 8, 5, 8, 9, 7, 3, 3, 9, 2, 7, 7, 5, 2, 8, 1, 5, 8, 6, 9, 6, 4, 7, 1, 5, 3, 0, 9, 8, 9, 3, 7, 2, 0, 7, 3, 9, 5, 7, 5, 6, 5, 6, 8, 2, 0, 8, 8, 8, 7, 9, 9, 7, 1, 6, 3, 9, 5, 3, 5, 5, 1, 0, 0, 8, 0, 0, 0, 4 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Equals the derivative of the Dirichlet eta function at x=0. - Stanislav Sykora, May 27 2015

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..5000

J.-F. Alcover, Plot of harmonic sum G(x) for x >= 0

Philippe Flajolet, Xavier Gourdon, and Philippe Dumas, Mellin Transforms and Asymptotics: Harmonic Sums.

Eric Weisstein's World of Mathematics, Dirichlet eta function

FORMULA

Given the harmonic sum G(x) = Sum_{k>=1} (-1)^k*log(k)*exp(-k^2*x), the limit when x->0 of G(x) is log(sqrt(Pi/2)).

Integral_{0..infinity} G(x) dx = (Pi^2/12)*log(2)+zeta'(2)/2 = (Pi^2/12)*(EulerGamma+log(4*Pi)-12*log(Glaisher)) = 0.1013165781635...

G'(0) = 7*zeta'(-2) = -7*zeta(3)/(4*Pi^2) = -0.2131391994...

EXAMPLE

0.22579135264472743236309761494744107178589733927752815869647153...

MATHEMATICA

RealDigits[Log[Sqrt[Pi/2]], 10, 105] // First

PROG

(PARI) log(sqrt(Pi/2)) \\ G. C. Greubel, Jan 09 2017

CROSSREFS

Cf. A069998.

Sequence in context: A216392 A239259 A188623 * A241761 A278388 A239737

Adjacent sequences:  A256355 A256356 A256357 * A256359 A256360 A256361

KEYWORD

nonn,cons,easy

AUTHOR

Jean-Fran├žois Alcover, Mar 26 2015

STATUS

approved

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Last modified March 30 18:30 EDT 2017. Contains 284302 sequences.