A double exponential function is a constant raised to the power of an exponential function. The general formula is , which grows much more quickly than an exponential function. For example, if a = b = 10:f(−1) ≈ 1.26f(0) = 10f(1) = 1010f(2) = 10100 = googolf(3) = 101000f(100) = 1010100 = googolplex.Factorials grow faster than exponential functions, but much slower than double-exponential functions. The hyper-exponential function and Ackermann function grow even faster.

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• A double exponential function is a constant raised to the power of an exponential function. The general formula is , which grows much more quickly than an exponential function. For example, if a = b = 10:f(−1) ≈ 1.26f(0) = 10f(1) = 1010f(2) = 10100 = googolf(3) = 101000f(100) = 1010100 = 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 the double exponential function is the double logarithm ln(ln(x)).
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