OFFSET
1,3
REFERENCES
Paul J. Nahin, "An Imaginary Tale, The Story of [Sqrt(-1)]," Princeton University Press, Princeton, NJ 1998, p. 188.
LINKS
Harry J. Smith, Table of n, a(n) for n = 1..20000
Antonio Gracia Llorente, Another Infinite Product for π/e, OSF Preprint, 2024.
Z. A. Melzak, Infinite Products for Pi*e and Pi/e, The American Mathematical Monthly, Vol. 68, No. 1 (Jan., 1961), pp. 39-41 (3 pages).
Solution of Problem 11771, The American Mathematical Monthly, 121 (2014).
FORMULA
Equals Integral_{-oo..oo} cos(x)/(1 + x^2) dx. - Robert G. Wilson v, Jan 15 2004
Equals Integral_{-oo..oo} cos(x)/(1 + x^2)^2 dx. - Amiram Eldar, Jul 21 2020
From Robert FERREOL, Apr 02 2022: (Start)
Equals Integral_{-oo..oo} x*sin(x)/(1 + x^2) dx.
Equals 2*Integral_{-oo..oo} x*sin(x)/(1 + x^2)^2 dx. (End)
Equals Product_{k>=1} ((2*k + 1)/(2*k - 1))^(2*k)*(k/(k + 1))^(2*k + 1). - Antonio Graciá Llorente, Mar 30 2024
Equals 1/A061360. - Alois P. Heinz, Jul 14 2024
EXAMPLE
Pi/e ~= 1.15572734979092171791009318331269629912...
MATHEMATICA
RealDigits[ Pi/E, 10, 110][[1]] (* Robert G. Wilson v, Jan 15 2004 *)
PROG
(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
CROSSREFS
KEYWORD
cons,nonn
AUTHOR
Jason Earls, Jun 08 2001
STATUS
approved