A composition of a function with itself gives a nested function , which gives , etc. Function nesting is implemented in Mathematica as Nest[f, expr, n], and a listing of incremental nestings is implemented as NestList[f, expr, n].

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

			(1)
			(2)

where is the exponential integral, the first two nestings of the natural logarithm give

			(3)
			(4)

where is the logarithmic integral.

CITE THIS AS:

Weisstein, Eric W. "Nested Function." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/NestedFunction.html