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A086729 Decimal expansion of Pi^2/72.

%I A086729 #31 May 26 2022 11:30:18
%S A086729 1,3,7,0,7,7,8,3,8,9,0,4,0,1,8,8,6,9,7,0,6,0,3,4,5,9,7,2,2,0,5,0,2,0,
%T A086729 9,9,1,0,1,5,7,9,1,5,8,4,3,3,8,9,9,8,6,9,8,1,1,2,9,6,5,1,9,1,1,4,1,6,
%U A086729 7,2,8,9,2,0,0,2,6,6,7,3,9,4,8,6,1,3,5,7,4,1,7,1,8,3,1,3,2,2,5
%N A086729 Decimal expansion of Pi^2/72.
%C A086729 The original name was: Decimal expansion of Sum_{m=0..infinity} 1/(6*m+3)^2.
%D A086729 L. Fejes Toth, Lagerungen in der Ebene, auf der Kugel und im Raum, 2nd. ed., Springer-Verlag, Berlin, Heidelberg 1972; see p. 213.
%H A086729 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>
%F A086729 Equals A111003/9. - _R. J. Mathar_, Dec 18 2010
%F A086729 From _Amiram Eldar_, Jul 19 2020: (Start)
%F A086729 Sum_{k>=0} (1/(12*k+3)^2 + 1/(12*k+9)^2).
%F A086729 Equals Integral_{x=1..oo} log(1 + 1/x^6)/x dx. (End)
%F A086729 Equals A353908/2. - _Omar E. Pol_, May 12 2022
%e A086729 0.1370778389040188697...
%p A086729 evalf(Pi^2/72) ;  # _R. J. Mathar_, Dec 18 2010
%o A086729 (PARI) Pi^2/72 \\ _Omar E. Pol_, May 12 2022
%Y A086729 Cf. A086722, A086723, A086724, A086725, A086726, A086727, A086728, A086730, A086731, A111003, A353908.
%K A086729 nonn,cons,easy
%O A086729 0,2
%A A086729 _N. J. A. Sloane_, Jul 31 2003
%E A086729 New name after _R. J. Mathar_'s Maple program. - _Omar E. Pol_, May 12 2022