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A019706 Decimal expansion of sqrt(Pi)/4.

%I A019706 #45 May 03 2024 03:00:46
%S A019706 4,4,3,1,1,3,4,6,2,7,2,6,3,7,9,0,0,6,8,2,4,5,4,1,8,7,0,8,3,5,2,8,6,2,
%T A019706 9,5,6,9,9,3,8,7,3,6,4,0,3,0,5,9,6,7,8,2,0,5,3,4,5,1,9,4,7,4,6,3,2,2,
%U A019706 7,8,2,1,1,4,7,7,5,8,0,4,5,3,4,3,7,3,7,6,6,4,1,8,4,6,3,6,1,6,6
%N A019706 Decimal expansion of sqrt(Pi)/4.
%H A019706 Ivan Panchenko, <a href="/A019706/b019706.txt">Table of n, a(n) for n = 0..1000</a>
%H A019706 I. S. Gradsteyn and I. M. Ryzhik, <a href="http://mathtable.com/gr/index.html">Table of integrals, series and products</a>, (1980), page 420 (formulas 3.757.1, 3.757.2).
%H A019706 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>
%F A019706 Equals sqrt(A019683). - _Michel Marcus_, Aug 31 2014
%F A019706 From _A.H.M. Smeets_, Sep 22 2018: (Start)
%F A019706 Equals Integral_{x >= 0} sin(8x)/sqrt(x) dx [Gradshteyn and Ryzhik].
%F A019706 Equals Integral_{x >= 0} cos(8x)/sqrt(x) dx [Gradshteyn and Ryzhik]. (End)
%F A019706 From _Amiram Eldar_, Aug 13 2020: (Start)
%F A019706 Equals Integral_{x=0..oo} x * exp(-x^4) dx.
%F A019706 Equals Integral_{x=0..oo} x^2 * exp(-x^2) dx. (End)
%e A019706 0.44311346272637900682454187083528629569938736403059678...
%p A019706 evalf(sqrt(Pi)/4,120); # _Muniru A Asiru_, Sep 22 2018
%t A019706 First[RealDigits[Sqrt[Pi]/4, 10, 100]] (* _Paolo Xausa_, May 02 2024 *)
%o A019706 (PARI) sqrt(Pi)/4 \\ _Altug Alkan_, Sep 22 2018
%o A019706 (PARI) intnum(x=0, [oo, -8*I], sin(8*x)/sqrt(x)) \\ _Gheorghe Coserea_, Sep 23 2018
%o A019706 (PARI) intnum(x=[0, -1/2], [oo, 8*I], cos(8*x)/sqrt(x)) \\ _Gheorghe Coserea_, Sep 23 2018
%Y A019706 Cf. A019683.
%K A019706 nonn,cons
%O A019706 0,1
%A A019706 _N. J. A. Sloane_