The exponential factorial of a positive integer n, denoted by n$, is n raised to the power of n − 1, which in turn is raised to the power of n − 2, and so on and so forth, that is,
The exponential factorial can also be defined with the recurrence relation
Like tetration, there is currently no accepted method of extension of the exponential factorial function to real and complex values of its argument, unlike the factorial function, for which such an extension is provided by the gamma function.
Related functions, notation and conventions
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