Randall Munroe defines Jenny's constant as the positive real number given by (7e - 1/e - 9)π² = 867.530901981...
(The rest of the digits can be found in sequence A182369 in The On-Line Encyclopedia of Integer Sequences)
The first seven digits of the constant are the same as those of Jenny's phone number in Tommy Tutone's classic song, "867-5309/Jenny". The ninth through twelfth digits are the same as those of the year the song was recorded, 1981. Hence, the name.
Eric Weisstein has found some simple approximations of Jenny's constant:
-
39eπ + 4π + ln 2 + 2 ln π - 40 tan-1 π = 867.53090001...
-
581 / 13π + 3531π/13 = 867.53090028...
-
-148e-1 + 63 + 316e = 867.53090050...
References
Munroe, Randall. "A Table of Slightly Wrong Equations and Identities Useful
for Approximations and/or Trolling Teachers." xkcd.
http://xkcd.com/1047/. Apr. 2012.
Weisstein, Eric W. "Jenny's Constant." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/JennysConstant.html