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A196877 Decimal expansion of Pi/2*(Pi^2/12 + (log(2))^2).

%I A196877 #30 Jun 12 2025 22:34:58
%S A196877 2,0,4,6,6,2,2,0,2,4,4,7,2,7,4,0,6,4,6,1,6,9,6,4,1,0,0,8,1,7,6,9,7,3,
%T A196877 4,7,6,6,3,7,4,4,1,9,5,3,4,9,4,6,5,6,2,6,0,6,1,0,2,6,8,5,5,2,7,2,5,9,
%U A196877 0,6,6,8,7,9,5,1,2,1,7,3,3,6,5,8,4,6,8,8,4,6,7,6,3,2,9,1,2,5,2,5,3,4,3,4,7
%N A196877 Decimal expansion of Pi/2*(Pi^2/12 + (log(2))^2).
%C A196877 The value of the integral_{x=0..Pi/2} log(sin(x))^2 dx. The value of sqrt(Pi)/2*(d^2/da^2(gamma((a+1)/2)/gamma(a/2+1))) at a=0. - _Seiichi Kirikami_ and _Peter J. C. Moses_, Oct 07 2011
%D A196877 I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series and Products, 4th edition, 3.621.1
%H A196877 G. C. Greubel, <a href="/A196877/b196877.txt">Table of n, a(n) for n = 1..10000</a>
%H A196877 K. S. Kolbig, <a href="https://doi.org/10.1090/S0025-5718-1983-0689472-3">On the integral int_0^Pi/2 log^n cos x log^p sin x dx</a>, Math. Comp. 40 (162) (1983) 565-570, r_{2,0}
%F A196877 Equals A019669*(A072691 + A002162^2).
%F A196877 Equals Integral_{x=0..1} log(x)^2/sqrt(1-x^2) dx. - _Amiram Eldar_, May 27 2023
%e A196877 2.04662202447274064616964100817...
%t A196877 RealDigits[N[Pi/2 (Pi^2/12 + Log[2]^2),150]][[1]]
%o A196877 (PARI) Pi/2*(Pi^2/12+(log(2))^2) \\ _Michel Marcus_, Jan 13 2015
%Y A196877 Cf. A002162, A019669, A072691, A173623, A196878.
%K A196877 cons,nonn
%O A196877 1,1
%A A196877 _Seiichi Kirikami_, Oct 07 2011