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2.2.6 Building Lists from Functions
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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