A double exponential function is a constant raised to the power of an exponential function. The general formula is , which grows even faster than an exponential function. For example, if a = b = 10:

  • f(−1) ≈ 1.26
  • f = 10
  • f(1) = 10
  • f(2) = 10 = googol
  • f(3) = 10
  • f(100) = 10 = googolplex.

Factorials grow faster than exponential functions, but much slower than double-exponential functions. The hyper-exponential function and Ackermann function grow even faster. See Big O notation for a comparison of the rate of growth of various functions.

The inverse of a double exponential function is a double logarithm.

From Wikipedia under the GNU Free Documentation License
Thu Jul 23 02:04:45 2009

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