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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

%I

%S 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,

%T 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,

%U 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

%N Decimal expansion of Pi^2*log(2)/8 - 7*zeta(3)/16, where zeta is the Riemann zeta function.

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

%H K. Onodera, <a href="http://dx.doi.org/10.1090/S0002-9947-2010-05176-1">Generalized log sine integrals and the Mordell-Tornheim zeta values</a>, Trans. Am. Math. Soc. 363 (3) (2010) 1463.

%F Equals A111003 * A002162 - 7*A002117/16.

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

%F sum_{n=1..infinity} (4^n / (8n^3 binomial(2n,n)). - _John Molokach_, Aug 01 2013

%e -0.3292361628498170682435494485830026...

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

%t N[(1/8) (Pi^2 Log[2] - 7 Zeta[3]/2), 100] (* _John Molokach_, Aug 02 2013 *)

%Y Cf. A046161.

%K cons,nonn

%O 0,1

%A _R. J. Mathar_, Nov 08 2010

%E A-number typo in formula corrected by _R. J. Mathar_, Nov 15 2010

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Last modified May 19 04:06 EDT 2019. Contains 323377 sequences. (Running on oeis4.)