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%I #32 Sep 08 2022 08:45:13
%S 1,1,7,8,0,9,7,2,4,5,0,9,6,1,7,2,4,6,4,4,2,3,4,9,1,2,6,8,7,2,9,8,1,3,
%T 5,8,1,5,7,3,9,3,8,5,2,4,7,6,5,6,6,4,6,8,2,8,6,5,6,0,4,2,2,2,1,1,5,4,
%U 3,1,1,5,2,3,5,7,3,2,8,3,7,4,4,8,5,5,1,3,0,5,9,5,0,3,2,9,3,9,0,0,4,9
%N Decimal expansion of (3*Pi)/8.
%C Area of an astroid with a = 1.
%H Harry J. Smith, <a href="/A093828/b093828.txt">Table of n, a(n) for n = 1..20000</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Astroid.html">Astroid</a>.
%H Eric W. Weisstein, <a href="https://mathworld.wolfram.com/EulersSeriesTransformation.html">Euler's Series Transformation</a>.
%H <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>
%F Equals Integral_{x>0} sin(x)^3/x^3. - _Jean-François Alcover_, Jun 04 2013
%F From _Amiram Eldar_, Aug 02 2020: (Start)
%F Equals arctan(1 + sqrt(2)).
%F Equals Integral_{x=0..1} x^(3/2)/sqrt(1-x) dx. (End)
%F Equals Sum_{k>=1} sin(k*Pi/4)/k. - _Amiram Eldar_, May 30 2021
%F 3*Pi/8 = Sum_{n >= 1} n*(n+1)*2^(n+1)/binomial(2*n+6,n+3) (apply Euler's series transformation to the series representation Pi = 384*Sum_{n >= 1} (-1)^(n+1)*n^2/((4*n^2 - 1)*(4*n^2 - 9)*(4*n^2 - 25)) ). - _Peter Bala_, Dec 08 2021
%e 1.1780972450961724644234912687298135815739385247656646...
%p evalf[110](3*Pi*(1/8)); # _G. C. Greubel_, Aug 11 2019
%t RealDigits[3*Pi/8, 10, 105][[1]] (* _G. C. Greubel_, Aug 11 2019 *)
%o (PARI) { default(realprecision, 20080); x=3*Pi/8; for (n=1, 20000, d=floor(x); x=(x-d)*10; write("b093828.txt", n, " ", d)); } \\ _Harry J. Smith_, Jun 18 2009
%o (Magma) SetDefaultRealField(RealField(110)); R:= RealField(); 3*Pi(R)/8; // _G. C. Greubel_, Aug 11 2019
%o (Sage) numerical_approx(3*pi/8, digits=110) # _G. C. Greubel_, Aug 11 2019
%Y Cf. A161685 (continued fraction). - _Harry J. Smith_, Jun 18 2009
%K nonn,cons,easy
%O 1,3
%A _Eric W. Weisstein_, Apr 16 2004
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