Double exponential function - Wikipedia
A double exponential function is a constant raised to the power of an exponential function. The general formula is π ( π₯ ) = π π π₯ = π ( π π₯ ) (where a>1 and b>1), which grows much more quickly than an exponential function. For example, if a = b = 10: 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)). The complex double exponential function is entire, because it is the composition of two entire functions π ( π₯ ) = π π₯ = π π₯ ln β‘ π and π ( π₯ ) = π π₯ = π π₯ ln β‘ π . A sequence of positive integers (or real numbers) is said to have double exponential rate of growth if the function giving the nth term of the sequence is bounded above and below by double exponential functions of n. Examples
Double exponential function - Wikipedia Jump to content From Wikipedia, the free encyclopedia Exponential function of an exponential function A double exponential function (red curve) compared to a single exponential function (blue curve). 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 ) {\displaystyle 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) = 10 10 x f (0) = 10 f (1) = 10 10 f (2) = 10 100 = goog
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