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A061382 Decimal expansion of Pi/e.

%I A061382 #83 Nov 02 2024 03:54:23
%S A061382 1,1,5,5,7,2,7,3,4,9,7,9,0,9,2,1,7,1,7,9,1,0,0,9,3,1,8,3,3,1,2,6,9,6,
%T A061382 2,9,9,1,2,0,8,5,1,0,2,3,1,6,4,4,1,5,8,2,0,4,9,9,7,0,6,5,3,5,3,2,7,2,
%U A061382 8,8,6,3,1,8,4,0,9,1,6,9,3,9,4,4,0,1,8,8,4,3,4,2,3,5,6,7,3,5,5,8,8,0,4,4,8
%N A061382 Decimal expansion of Pi/e.
%D A061382 Paul J. Nahin, "An Imaginary Tale, The Story of [Sqrt(-1)]," Princeton University Press, Princeton, NJ 1998, p. 188.
%H A061382 Harry J. Smith, <a href="/A061382/b061382.txt">Table of n, a(n) for n = 1..20000</a>
%H A061382 David J. Jeffrey, <a href="https://doi.org/10.5206/mt.v4i3.19795">Problems, Puzzles and Challenges</a>, Maple Transactions Vol. 4 No. 3 (2024).
%H A061382 Antonio Gracia Llorente, <a href="https://osf.io/preprints/osf/vdu4t">Another Infinite Product for π/e</a>, OSF Preprint, 2024.
%H A061382 Z. A. Melzak, <a href="https://www.jstor.org/stable/2311360">Infinite Products for Pi*e and Pi/e</a>, The American Mathematical Monthly, Vol. 68, No. 1 (Jan., 1961), pp. 39-41 (3 pages).
%H A061382 Solution of <a href="http://www.jstor.org/discover/10.4169/amer.math.monthly.121.04.365">Problem 11771</a>, The American Mathematical Monthly, 121 (2014).
%H A061382 Zander, <a href="https://math.stackexchange.com/a/349506">Integrate Integral_{x=0..1} x^(-x) (1-x)^(x-1) sin(Pi x) dx</a>, MathStackExchange Apr. 2013.
%F A061382 Equals A000796 / A001113.
%F A061382 Equals Integral_{-oo..oo} cos(x)/(1 + x^2) dx. - _Robert G. Wilson v_, Jan 15 2004
%F A061382 Equals Integral_{-oo..oo} cos(x)/(1 + x^2)^2 dx. - _Amiram Eldar_, Jul 21 2020
%F A061382 From _Robert FERREOL_, Apr 02 2022: (Start)
%F A061382 Equals Integral_{-oo..oo} x*sin(x)/(1 + x^2) dx.
%F A061382 Equals 2*Integral_{-oo..oo} x*sin(x)/(1 + x^2)^2 dx. (End)
%F A061382 Equals Product_{k>=1} ((2*k + 1)/(2*k - 1))^(2*k)*(k/(k + 1))^(2*k + 1). - _Antonio Graciá Llorente_, Mar 30 2024
%F A061382 Equals 1/A061360. - _Alois P. Heinz_, Jul 14 2024
%F A061382 Equals Integral_{x=0..1} sin(Pi*x)/(x^x*(1 - x)^(1 - x)) dx. (See Zander link). - _Peter Luschny_, Oct 31 2024
%e A061382 Pi/e ~= 1.15572734979092171791009318331269629912...
%t A061382 RealDigits[ Pi/E, 10, 110][[1]] (* _Robert G. Wilson v_, Jan 15 2004 *)
%o A061382 (PARI) { default(realprecision, 20080); x=Pi/exp(1); for (n=1, 20000, d=floor(x); x=(x-d)*10; write("b061382.txt", n, " ", d)) } \\ _Harry J. Smith_, Jul 22 2009
%Y A061382 Cf. A061666 (continued fraction for Pi/e).
%Y A061382 Cf. A001113, A000796, A061360.
%K A061382 cons,nonn
%O A061382 1,3
%A A061382 _Jason Earls_, Jun 08 2001