A086729 - OEIS

%I #31 May 26 2022 11:30:18

%S 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 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 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 Decimal expansion of Pi^2/72.

%C The original name was: Decimal expansion of Sum_{m=0..infinity} 1/(6*m+3)^2.

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

%H <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>

%F Equals A111003/9. - _R. J. Mathar_, Dec 18 2010

%F From _Amiram Eldar_, Jul 19 2020: (Start)

%F Sum_{k>=0} (1/(12*k+3)^2 + 1/(12*k+9)^2).

%F Equals Integral_{x=1..oo} log(1 + 1/x^6)/x dx. (End)

%F Equals A353908/2. - _Omar E. Pol_, May 12 2022

%e 0.1370778389040188697...

%p evalf(Pi^2/72) ;  # _R. J. Mathar_, Dec 18 2010

%o (PARI) Pi^2/72 \\ _Omar E. Pol_, May 12 2022

%Y Cf. A086722, A086723, A086724, A086725, A086726, A086727, A086728, A086730, A086731, A111003, A353908.

%K nonn,cons,easy

%O 0,2

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

%E New name after _R. J. Mathar_'s Maple program. - _Omar E. Pol_, May 12 2022