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A152584 Decimal expansion of (Pi^3)/24.

%I A152584 #21 Sep 30 2022 23:10:52
%S A152584 1,2,9,1,9,2,8,1,9,5,0,1,2,4,9,2,5,0,7,3,1,1,5,1,3,1,2,7,7,9,5,8,9,1,
%T A152584 4,6,6,7,5,9,3,8,7,0,2,3,5,7,8,5,4,6,1,5,3,9,2,2,6,8,9,0,8,7,6,5,8,5,
%U A152584 9,9,7,8,8,2,2,7,7,3,7,7,5,1,5,6,5,2,7,9,2,0,9,6,9,1,7,8,6,9,2,4,7,0,9,5,8
%N A152584 Decimal expansion of (Pi^3)/24.
%C A152584 Consider infinite sum made of areas of circles Pi*radius^2 with diameter 1/n.
%C A152584 The volume is (Pi/4)*(1 + 1/4 + 1/9 + 1/16 + 1/25 + ... + 1/n^2)
%C A152584 = (1 - 1/3 + 1/5 - 1/7 + 1/9 - 1/11 + ...)*(1 + 1/4 + 1/9 + 1/16 + 1/25 + ...)
%C A152584 = (Pi/4) * (Pi^2/6) = Pi^3/24.
%C A152584 Equals volume of a cone of height Pi^2/8 and radius 1.
%C A152584 Equals volume of a sphere (4*Pi*Pi^2/32)/3 with radius^3 = (Pi^2/32).
%H A152584 G. C. Greubel, <a href="/A152584/b152584.txt">Table of n, a(n) for n = 1..5000</a>
%H A152584 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>
%F A152584 Equals Integral_{x=0..oo} arctan(x)^2/(x^2 + 1) dx. - _Amiram Eldar_, Aug 06 2020
%e A152584 1.291928195012492507311513127795891466759387023578...
%t A152584 RealDigits[(Pi^3)/24, 10, 50][[1]] (* _G. C. Greubel_, Jun 09 2017 *)
%o A152584 (PARI) (Pi^3)/24 \\ _G. C. Greubel_, Jun 09 2017
%Y A152584 Cf. A013661, A003881, A102753, A019679, A111003.
%K A152584 cons,nonn
%O A152584 1,2
%A A152584 _Eric Desbiaux_, Dec 08 2008