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Concept
Double exponential function
Summary
A double exponential function is a constant raised to the power of an exponential function. The general formula is f(x) = a^{b^x}=a^{(b^x)} (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 doubly 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)).
Doubly exponential sequences
A sequence of positive integers (or real numbers) is said to have doubly exponential rate of growth if the function giving the nth term of the sequence is bounded above and below by doubly exponential functions of n.
Examples inc
Official source
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