TOPICS
e Approximations
An amazingpandigital approximation to
that is correct to 18457734525360901453873570 decimal digits is given by
 | (1) |
found by R. Sabey in 2004 (Friedman 2004).
Castellanos (1988ab) gives several curious approximations to
,
 |  |  | (2) |
 |  |  | (3) |
 |  |  | (4) |
 |  |  | (5) |
 |  |  | (6) |
 |  |  | (7) |
which are good to 6, 7, 9, 10, 12, and 15 digits respectively.
E. Pegg Jr. (pers. comm., Mar. 2, 2002), found
 | (8) |
which is good to 7 digits.
J. Lafont (pers. comm., MAy 16, 2008) found
 | (9) |
where
is aharmonic number, which is good to 7 digits.
N. Davidson (pers. comm., Sept. 7, 2004) found
 | (10) |
which is good to 6 digits.
D. Barron noticed the curious approximation
 | (11) |
where
isCatalan's constant and
is theEuler-Mascheroni constant, which however, is only good to 3 digits.
See also
Almost Integer,eExplore with Wolfram|Alpha
More things to try:
References
Castellanos, D. "The Ubiquitous Pi. Part I."Math. Mag.61, 67-98, 1988.Friedman, E. "Problem of the Month (August 2004)."https://erich-friedman.github.io/mathmagic/0804.html.Referenced on Wolfram|Alpha
e ApproximationsCite this as:
Weisstein, Eric W. "e Approximations."FromMathWorld--A Wolfram Web Resource.https://mathworld.wolfram.com/eApproximations.html