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A152651 Decimal expansion of 3*Zeta(5) - Zeta(3)*Pi^2/6. 10

%I

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

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

%U 9,5,7,3,5,2,1,2,2,4,0,2,4,5,9,7,7,7,4,4,9,4,7,1,4,9,6,5,0,4,0,1,7,6,6,7,6

%N Decimal expansion of 3*Zeta(5) - Zeta(3)*Pi^2/6.

%C A division by 2 is missing in Mezo's penultimate formula on page 4.

%H David Borwein and J. M. Borwein, <a href="http://dx.doi.org/10.1090/S0002-9939-1995-1231029-X">On an intriguing integral and some series related to zeta(4)</a>, Proc. Am. Math. Soc. 123 (1995) 1191-1198.

%H Istvan Mezo, <a href="http://arxiv.org/abs/0811.0042">Summation of Hyperharmonic Numbers</a>, arXiv:0811.0042 [math.CO], 2008.

%F Equals Sum_(j >= 1) H(j)/j^4 = where H(j) = A001008(j)/A002805(j).

%F Equals 3*A013663 - A002117*A013661.

%e Equals 1.1334789151328136607970110178859769320890912918456042272...

%o (PARI) 3*zeta(5) - zeta(3)*Pi^2/6 \\ _Michel Marcus_, Jul 07 2015

%K cons,easy,nonn

%O 1,3

%A _R. J. Mathar_, Dec 10 2008

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Last modified April 23 07:51 EDT 2019. Contains 322381 sequences. (Running on oeis4.)