Acomposition of a function with itself gives a nested function, which gives, etc. Function nesting is implemented in theWolfram Language asNest[f,expr,n], and a listing of incremental nestings is implemented asNestList[f,expr,n].

Integrals of nested functions rapidly become difficult to find in exact form. For example, the first two nestings of theexponential function gives

			(1)
			(2)

where is theexponential integral, the first two nestings of thenatural logarithm give

			(3)
			(4)

where is thelogarithmic integral.

See also

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Cite this as:

Weisstein, Eric W. "Nested Function."FromMathWorld--A Wolfram Resource.https://mathworld.wolfram.com/NestedFunction.html

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