A086723 - OEIS

%I #6 Feb 12 2013 08:31:18

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

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

%U 2,3,8,9,6,3,0,6,2,7,6,9,5,6,2,9,2,0,6,9,0,0,1,2,2,2,7,2,7,5,7

%N Decimal expansion of 1/(g(1)+g(2)-g(4)-g(5)), where g(k) = sum(1/(6*m+k)^2,m=0..infinity).

%D L. Fejes Toth, Lagerungen in der Ebene, auf der Kugel und im Raum, 2nd. ed., Springer-Verlag, Berlin, Heidelberg 1972; see p. 213.

%e .85327608831408080...

%t g[k_] := PolyGamma[1, k/6]/36; First[ RealDigits[1/(g[1] + g[2] - g[4] - g[5]), 10, 99]] (* _Jean-François Alcover_, Feb 12 2013 *)

%Y Cf. A086722-A086731.

%K nonn,cons

%O 0,1

%A _N. J. A. Sloane_, Jul 31 2003