e Approximations

An amazing pandigital 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 a harmonic 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 is Catalan's constant and is the Euler-Mascheroni constant, which however, is only good to 3 digits.