%I #46 Sep 28 2022 13:38:50

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

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

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

%N Decimal expansion of Pi^2/24.

%D George Boros and Victor H. Moll, Irresistible integrals, Cambridge University Press, 2006, p. 242.

%D Ovidiu Furdui, Limits, Series, and Fractional Part Integrals: Problems in Mathematical Analysis, New York: Springer, 2013. See Problem 3.45, p. 158 and 199-200.

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

%F Equals Integral_{x=0..Pi/2} log(sec(x))/tan(x) dx.

%F Equals Sum_{k >= 1} 1/(2k)^2. - _Geoffrey Critzer_, Nov 02 2013

%F Equals (1/10) * Sum_{k>=1} d(k^2)/k^2, where d(k) is the number of divisors of k (A000005). - _Amiram Eldar_, Jun 27 2020

%F Equals Sum_{n >= 0} 1/((2*n+1)*(6*n+3)). - _Peter Bala_, Feb 02 2022

%F Equals Sum_{n>=0} ((-1)^n * (Sum_{k>=n+1} (-1)^k/k)^2) (Furdui, 2013). - _Amiram Eldar_, Mar 26 2022

%e 0.411233516712056609118103791661506297304737475301699609433889557342501867600...

%t RealDigits[Pi^2/24, 10, 100] // First

%o (Magma) pi:=Pi(RealField(110)); Reverse(Intseq(Floor(10^100*(pi)^2/24))); // _Vincenzo Librandi_, Sep 25 2015

%o (PARI) Pi^2/24 \\ _Michel Marcus_, Dec 10 2020

%Y Cf. A000005, A013679, A111003, A072691, A078471.

%K nonn,cons,easy

%O 0,1

%A _Jean-François Alcover_, May 13 2013

%E Leading 0 term removed (to make offset correct) by _Rick L. Shepherd_, Jan 01 2014