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A173624 Decimal expansion of Pi^2*log(2)/8 - 7*zeta(3)/16, where zeta is the Riemann zeta function. 4
3, 2, 9, 2, 3, 6, 1, 6, 2, 8, 4, 9, 8, 1, 7, 0, 6, 8, 2, 4, 3, 5, 4, 9, 4, 4, 8, 5, 8, 3, 0, 0, 2, 6, 3, 7, 9, 5, 2, 7, 9, 0, 8, 7, 8, 1, 2, 4, 5, 2, 0, 9, 2, 8, 6, 3, 1, 3, 9, 7, 6, 7, 5, 6, 0, 2, 5, 8, 5, 4, 3, 9, 8, 3, 3, 8, 3, 4, 1, 1, 3, 8, 8, 1, 6, 6, 9, 3, 1, 8, 5, 3, 1, 5, 6, 4, 9, 9, 7, 2, 7, 8, 2, 2, 0 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

The absolute value of the integral {x=0..Pi/2} x*log(sin(x)) dx.

LINKS

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

K. Onodera, Generalized log sine integrals and the Mordell-Tornheim zeta values, Trans. Am. Math. Soc. 363 (3) (2010) 1463.

FORMULA

Equals A111003 * A002162 - 7*A002117/16.

sum_{n=1..Infinity} (phi(-1,1,2n)/(2n-1)^2), where phi is the Lerch transcendent. - John Molokach, Jul 22 2013

sum_{n=1..infinity} (4^n / (8n^3 binomial(2n,n)). - John Molokach, Aug 01 2013

EXAMPLE

-0.3292361628498170682435494485830026...

MAPLE

7*Zeta(3)/16-Pi^2*log(2)/8 ; evalf(%) ;

MATHEMATICA

N[(1/8) (Pi^2 Log[2] - 7 Zeta[3]/2), 100] (* John Molokach, Aug 02 2013 *)

CROSSREFS

Cf. A046161.

Sequence in context: A010271 A291777 A143074 * A182023 A228936 A169862

Adjacent sequences:  A173621 A173622 A173623 * A173625 A173626 A173627

KEYWORD

cons,nonn

AUTHOR

R. J. Mathar, Nov 08 2010

EXTENSIONS

A-number typo in formula corrected by R. J. Mathar, Nov 15 2010

STATUS

approved

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Last modified April 20 17:54 EDT 2019. Contains 322310 sequences. (Running on oeis4.)