A256319 - OEIS

A256319

Decimal expansion of Sum_{k>=0} (zeta(2k)/(2k+1))*(3/4)^(2k) (negated).

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

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OFFSET

0,2

LINKS

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

H. M. Srivasata, M. L. Glasser, Victor S. Adamchik, Some Definite Integrals Associated with the Riemann Zeta Function

FORMULA

Equals G/(3*Pi) - log(2)/4, where G is Catalan's constant.

EXAMPLE

-0.0760998271297134006415132115417458357308529822614513901...

MATHEMATICA

Join[{0}, RealDigits[Catalan/(3 Pi) - Log[2]/4, 10, 102] // First]

PROG

(PARI) suminf(k=0, (zeta(2*k)/(2*k+1))*(3/4)^(2*k)) \\ Michel Marcus, Mar 23 2015

(PARI) default(realprecision, 100); Catalan/(3*Pi) - log(2)/4 \\ G. C. Greubel, Aug 25 2018

(Magma) SetDefaultRealField(RealField(100)); R:=RealField(); Catalan(R)/(3*Pi(R)) - Log(2)/4; // G. C. Greubel, Aug 25 2018

CROSSREFS

Cf. A006752, A256318.

Sequence in context: A094123 A132799 A154580 * A324688 A334400 A309700

Adjacent sequences: A256316 A256317 A256318 * A256320 A256321 A256322

KEYWORD

nonn,cons,easy

AUTHOR

Jean-François Alcover, Mar 23 2015

STATUS

approved