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A222171 Decimal expansion of Pi^2/24.

%I A222171 #51 Jan 23 2025 13:06:27
%S A222171 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 A222171 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 A222171 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 A222171 Decimal expansion of Pi^2/24.
%D A222171 George Boros and Victor H. Moll, Irresistible integrals, Cambridge University Press, 2006, p. 242.
%D A222171 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 A222171 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>
%F A222171 Equals Integral_{x=0..Pi/2} log(sec(x))/tan(x) dx.
%F A222171 Equals Sum_{k >= 1} 1/(2k)^2. - _Geoffrey Critzer_, Nov 02 2013
%F A222171 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 A222171 Equals Sum_{n >= 0} 1/((2*n+1)*(6*n+3)). - _Peter Bala_, Feb 02 2022
%F A222171 Equals Sum_{n>=0} ((-1)^n * (Sum_{k>=n+1} (-1)^k/k)^2) (Furdui, 2013). - _Amiram Eldar_, Mar 26 2022
%F A222171 Equals Sum_{n>=1} A369180(n)/n^2. - _Friedjof Tellkamp_, Jan 23 2025
%e A222171 0.411233516712056609118103791661506297304737475301699609433889557342501867600...
%t A222171 RealDigits[Pi^2/24, 10, 100] // First
%o A222171 (Magma) pi:=Pi(RealField(110)); Reverse(Intseq(Floor(10^100*(pi)^2/24))); // _Vincenzo Librandi_, Sep 25 2015
%o A222171 (PARI) Pi^2/24 \\ _Michel Marcus_, Dec 10 2020
%Y A222171 Cf. A000005, A013679, A111003, A072691, A078471, A369180.
%K A222171 nonn,cons,easy
%O A222171 0,1
%A A222171 _Jean-François Alcover_, May 13 2013
%E A222171 Leading 0 term removed (to make offset correct) by _Rick L. Shepherd_, Jan 01 2014