cp's OEIS Frontend

A210958 Decimal expansion of 1 - (Pi/4).

%I A210958 #44 Jun 13 2025 05:46:42
%S A210958 2,1,4,6,0,1,8,3,6,6,0,2,5,5,1,6,9,0,3,8,4,3,3,9,1,5,4,1,8,0,1,2,4,2,
%T A210958 7,8,9,5,0,7,0,7,6,5,0,1,5,6,2,2,3,5,4,4,7,5,6,2,6,3,8,5,1,9,2,3,0,4,
%U A210958 5,8,9,8,4,2,8,4,4,7,7,5,0,3,4,2,9,9,1
%N A210958 Decimal expansion of 1 - (Pi/4).
%C A210958 Decimal expansion of (4 - Pi)/4.
%C A210958 Area between a square and the inscribed quarter circle of radius 1.
%C A210958 Also area between a circle of radius 1 and the circumscribed square, divided by 4.
%C A210958 Also area between a circle of diameter 1 and the circumscribed square. - _Omar E. Pol_, Sep 24 2013
%C A210958 Also volume between a cube of side length 1 and the inscribed cylinder. - _Omar E. Pol_, Sep 25 2013
%H A210958 M. L. Glasser, <a href="https://doi.org/10.1080/00029890.2019.1565856">A note on Beukers's and related integrals</a>, Amer. Math. Monthly 126(4) (2019), 361-363.
%H A210958 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>
%F A210958 1 - (Pi/4) = (4 - Pi)/4 = 1 - A003881 = A153799/4.
%F A210958 From _Amiram Eldar_, Jun 29 2020: (Start)
%F A210958 Equals Sum_{k>=0} (-1)^k/(2*k+3).
%F A210958 Equals Integral_{x=0..Pi/4} tan(x)^2 dx.
%F A210958 Equals Integral_{x=0..1} arcsin(x) dx /(1+x)^2.
%F A210958 Equals Integral_{x=1..oo} dx/(x^2+x^4). (End)
%F A210958 Equals -Integral_{x=0..1, y=0..1} arcsin(x*y)/((1+x*y)^2*log(x*y)) dx dy. (Apply Theorem 1 or Theorem 2 from Glasser (2019) to one of _Amiram Eldar_'s integrals.) - _Petros Hadjicostas_, Jun 29 2020
%F A210958 Continued fraction 1/(3 + 3^2/(2 + 5^2/(2 + 7^2/(2 + ... )))). - _Peter Bala_, Feb 28 2024
%e A210958 0.21460183660255169038433915418012427895070765015622...
%t A210958 RealDigits[1 - Pi/4, 10, 87][[1]] (* _Bruno Berselli_, Aug 03 2012 *)
%o A210958 (PARI) 1-Pi/4 \\ _Charles R Greathouse IV_, Oct 01 2022
%Y A210958 Cf. A003881, A153799.
%Y A210958 Essentially the same as A091651.
%K A210958 nonn,cons
%O A210958 0,1
%A A210958 _Omar E. Pol_, Aug 02 2012
%E A210958 More terms from _David Scambler_, Aug 02 2012