This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.
 MATHEMATICA TUTORIAL Related Tutorials »| Functions »

# Building Lists from Functions

 Array[f,n] generate a length n list of the form Array[f,{n1,n2,...}] generate an ××... nested list, each of whose entries consists of f applied to its indices NestList[f,x,n] generate a list of the form , where f is nested up to n deep FoldList[f,x,{a,b,...}] generate a list of the form ComposeList[{f1,f2,...},x] generate a list of the form

Making lists from functions.

This makes a list of 5 elements, each of the form p[i].
 Out[1]=
Here is another way to produce the same list.
 Out[2]=
This produces a list whose elements are .
 Out[3]=
This generates a 2×3 matrix whose entries are .
 Out[4]=
This generates a 3×3 matrix whose elements are the squares of the sums of their indices.
 Out[5]=
NestList and FoldList were discussed in "Applying Functions Repeatedly". Particularly by using them with pure functions, you can construct some very elegant and efficient Mathematica programs.
This gives a list of results obtained by successively differentiating with respect to .
 Out[6]=