A091474 - OEIS

%I #22 Oct 01 2022 13:50:43

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

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

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

%N Decimal expansion of Pi^2 * (2-sqrt(2))/32.

%H G. C. Greubel, <a href="/A091474/b091474.txt">Table of n, a(n) for n = 0..10000</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/DefiniteIntegral.html">Definite Integral</a>.

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

%F Equals Integral_{t=0..1} t^2 * log(t)/((t^2 - 1)*(t^4 + 1)) dt.

%F Equals Sum_{k>=1} 1/A047621(k)^2. - _Amiram Eldar_, Apr 17 2022

%e 0.18067126259065494279230812898167161533711457101829...

%t RealDigits[Pi^2 (2-Sqrt[2])/32,10,120][[1]] (* _Harvey P. Dale_, Nov 18 2013 *)

%o (PARI) default(realprecision, 100); Pi^2*(2-sqrt(2))/32 \\ _G. C. Greubel_, Oct 01 2018

%o (Magma) SetDefaultRealField(RealField(100)); R:= RealField(); Pi(R)^2*(2-Sqrt(2))/32; // _G. C. Greubel_, Oct 01 2018

%Y Cf. A047621.

%K nonn,cons

%O 0,2

%A _Eric W. Weisstein_, Jan 13 2004