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%I #13 May 31 2021 03:24:08
%S 1,2,0,5,7,9,9,6,4,8,6,7,8,3,2,6,3,4,0,1,5,7,4,1,2,2,5,2,6,0,9,4,9,8,
%T 7,0,2,3,0,8,7,6,1,2,2,2,0,0,6,6,4,3,0,7,6,9,9,4,5,0,9,8,1,5,1,4,8,0,
%U 2,6,4,6,9,0,1,2,5,5,5,2,3,4,7,9,4,2,6,0,5,9,5,7,1,2,3,3,4,4,6,3,0,6,2,2,8,2,5,2
%N Decimal expansion of Sum_{k>=1} coth(Pi*k)/k^3.
%C Splitting the infinite sum Simon Plouffe unearthed a rapidly converging series for zeta(3).
%D Bruce C. Berndt, Ramanujan Notebook part II, Infinite series, Springer Verlag, p. 293.
%H Simon Plouffe, <a href="http://plouffe.fr/simon/articles/Identities.pdf">Formulae for zeta(2n+1)</a>.
%F Equals 7*Pi^3/180.
%e 1.20579964867832634015741225260949870230876122200664...
%t RealDigits[7*Pi^3/180, 10, 100][[1]] (* _Amiram Eldar_, May 31 2021 *)
%o (PARI) 7*Pi^3/180
%Y Cf. A000796.
%K cons,nonn
%O 1,2
%A _Benoit Cloitre_, Jun 21 2003
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