Double exponential function
Exponential function of an exponential function / From Wikipedia, the free encyclopedia
A double exponential function is a constant raised to the power of an exponential function. The general formula is (where a>1 and b>1), which grows much more quickly than an exponential function. For example, if a = b = 10:
- f(x) = 1010x
- f(0) = 10
- f(1) = 1010
- f(2) = 10100 = googol
- f(3) = 101000
- f(100) = 1010100 = googolplex.
Factorials grow faster than exponential functions, but much more slowly than double exponential functions. However, tetration and the Ackermann function grow 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 log(log(x)).