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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]=