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%I #30 Sep 28 2022 13:44:11
%S 1,9,6,3,4,9,5,4,0,8,4,9,3,6,2,0,7,7,4,0,3,9,1,5,2,1,1,4,5,4,9,6,8,9,
%T 3,0,2,6,2,3,2,3,0,8,7,4,6,0,9,4,4,1,1,3,8,1,0,9,3,4,0,3,7,0,1,9,2,3,
%U 8,5,2,5,3,9,2,8,8,8,0,6,2,4,1,4,2,5,2,1,7,6,5,8,3,8,8,2,3,1,6
%N Decimal expansion of Pi/16.
%H Ivan Panchenko, <a href="/A019683/b019683.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>
%F From _Peter Bala_, Oct 27 2019: (Start)
%F Equals Integral_{x = 0..1} x^2*sqrt(1 - x^2) dx = Integral_{x = 0..1} x^3*sqrt(1 - x^8) dx.
%F Equals Integral_{x = 0..inf} x^2/(1 + x^2)^3 dx. (End)
%F From _Amiram Eldar_, Aug 04 2020: (Start)
%F Equals Sum_{k>=1} sin(k)^3 * cos(k)/k.
%F Equals Sum_{k>=1} sin(k)^3 * cos(k)^2/k.
%F Equals Sum_{k>=1} (-1)^(k+1) * sin((2*k-1)/4)/(2*k-1)^2. (End)
%e Pi/16 = 0.19634954084936207740391521145496893026232308746094411381... - _Vladimir Joseph Stephan Orlovsky_, Dec 02 2009
%t RealDigits[N[Pi/16,6! ]] (* _Vladimir Joseph Stephan Orlovsky_, Dec 02 2009 *)
%o (PARI) default(realprecision, 100); Pi/16 \\ _G. C. Greubel_, Aug 26 2019
%o (Magma) R:= RealField(100); Pi(R)/16; // _G. C. Greubel_, Aug 26 2019
%o (Sage) numerical_approx(pi/16, digits=100) # _G. C. Greubel_, Aug 26 2019
%Y Cf. A157332, A000796, A003881, A019669, A019670, A019675, A019679, A244978.
%K nonn,cons
%O 0,2
%A _N. J. A. Sloane_
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