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%I #23 Oct 01 2018 03:30:50
%S 5,2,6,9,3,9,1,1,3,5,4,1,2,6,3,6,1,9,2,1,7,2,1,8,7,3,3,8,8,4,0,3,7,0,
%T 9,1,9,6,3,8,5,0,9,0,0,3,0,6,4,6,9,9,1,8,9,0,3,7,3,8,5,0,3,7,4,4,7,2,
%U 8,9,1,3,5,8,8,5,0,3,7,0,5,8,0,9,2,3,2,0,1,4,6,3,1,7,8,4,4,4,0,6,7,3
%N Decimal expansion of -PolyGamma(2,(1+sqrt(3))/2)/2.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/RamanujanContinuedFractions.html">Ramanujan Continued Fractions</a>
%F Equals 2*Integral_{x >= 0} x^2*csch(x)/e^(sqrt(3)*x) dx.
%e 0.526939113...
%t RealDigits[-PolyGamma[2,(1+Sqrt[3])/2]/2,10,100][[1]] (* _Vaclav Kotesovec_, Aug 15 2015 *)
%o (PARI)
%o polygamma(n, x) = if (n == 0, psi(x), (-1)^(n+1)*n!*zetahurwitz(n+1, x));
%o -polygamma(2,(1+sqrt(3))/2)/2 \\ _Gheorghe Coserea_, Sep 30 2018
%o (PARI)
%o 2*intnum(x=0, [oo, 11/4], x^2/(sinh(x)*exp(sqrt(3)*x))) \\ _Gheorghe Coserea_, Sep 30 2018
%Y Cf. A091659.
%K nonn,cons
%O 0,1
%A _Eric W. Weisstein_, Jan 26 2004
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