2.2.6 Building Lists from Functions

 Array[f, n] generate a length n list of the form {f[1], f[2], ... } Array[f, {, , ... }] 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 {x, f[x], f[f[x]], ... }, where f is nested up to n deep FoldList[f, x, {a, b, ... }] generate a list of the form {x, f[x, a], f[f[x, a], b], ... } ComposeList[{, , ... }, x] generate a list of the form {x, [x], [[x]], ... }

Making lists from functions.
This makes a list of 5 elements, each of the form p[i].
 In[1]:=  Array[p, 5]
 Out[1]=
Here is another way to produce the same list.
 In[2]:=  Table[p[i], {i, 5}]
 Out[2]=
This produces a list whose elements are .
 In[3]:=  Array[ # + #^2 &, 5]
 Out[3]=
This generates a matrix whose entries are m[i, j].
 In[4]:=  Array[m, {2, 3}]
 Out[4]=
This generates a matrix whose elements are the squares of the sums of their indices.
 In[5]:=  Array[Plus[##]^2 &, {3, 3}]
 Out[5]=

NestList and FoldList were discussed in Section 2.2.2. 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 .
 In[6]:=  NestList[ D[#, x]&, x^n, 3 ]
 Out[6]=

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