Superfunction

In mathematics, superfunction is a nonstandard name for an iterated function for complexified continuous iteration index. Roughly, for some function f and for some variable x, the superfunction could be defined by the expression

Then, S(z;x) can be interpreted as the superfunction of the function f(x). Such a definition is valid only for a positive integer index z. The variable x is often omitted. Much study and many applications of superfunctions employ various extensions of these superfunctions to complex and continuous indices; and the analysis of the existence, uniqueness and their evaluation. The Ackermann functions and tetration can be interpreted in terms of super-functions.

单词	Superfunction
释义	Superfunction 英语百科 Superfunction In mathematics, superfunction is a nonstandard name for an iterated function for complexified continuous iteration index. Roughly, for some function f and for some variable x, the superfunction could be defined by the expression Then, S(z;x) can be interpreted as the superfunction of the function f(x). Such a definition is valid only for a positive integer index z. The variable x is often omitted. Much study and many applications of superfunctions employ various extensions of these superfunctions to complex and continuous indices; and the analysis of the existence, uniqueness and their evaluation. The Ackermann functions and tetration can be interpreted in terms of super-functions.
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