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%I #17 Apr 10 2024 09:14:47
%S 5,5,6,8,3,2,7,9,9,6,8,3,1,7,0,7,8,4,5,2,8,4,8,1,7,9,8,2,1,1,8,8,3,5,
%T 7,0,2,0,1,3,6,2,4,3,9,0,2,8,3,2,4,3,9,1,0,7,5,3,6,7,5,8,1,8,8,2,9,7,
%U 4,5,5,3,3,6,4,7,7,9,5,7,0,2,2,1,2,1,7,7,6,8,7,3,8,4,7,0,8,4,9,4,0,9,7,0,6
%N Decimal expansion of Pi^(3/2).
%C Log(Pi^(3/2)) = 1.5*log(Pi) = 1.5 * A053510 = 1.7170948...
%H Marc Chamberland and Armin Straub, <a href="https://doi.org/10.1016/j.aam.2013.07.003">On gamma quotients and infinite products</a>, Advances in Applied Mathematics, Vol. 51, No. 5 (2013), pp. 546-562, see pp. 555-556; <a href="http://arxiv.org/abs/1309.3455">arXiv preprint</a>, arXiv:1309.3455 [math.NT], 2013, see pp. 9-10.
%H <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%F Equals A000796 * A002161 = A002388 / A002161.
%F From _Vaclav Kotesovec_, Dec 10 2015: (Start)
%F Equals Gamma(3/14)*Gamma(5/14)*Gamma(13/14)/2.
%F Equals Gamma(1/14)*Gamma(9/14)*Gamma(11/14)/4.
%F (End)
%F Equals Integral_{x=-oo..oo, y=-oo..oo, z=-oo..oo} exp(-x^2 - y^2 - z^2) dx dy dz. - _Ilya Gutkovskiy_, Apr 10 2024
%e 5.5683279968317078452848179..
%p Pi^(3/2) ; evalf(%) ;
%t RealDigits[Pi^(3/2), 10, 120][[1]] (* _Amiram Eldar_, Jun 13 2023 *)
%Y Cf. A000796, A002161, A002388, A053510.
%K cons,easy,nonn
%O 1,1
%A _R. J. Mathar_, May 25 2010
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