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]. | |
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| Here is another way to produce the same list. | |
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Table[p[i], {i, 5}]
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This produces a list whose elements are  . | |
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Array[ # + #^2 &, 5]
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This generates a  matrix whose entries are m[i, j]. | |
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This generates a  matrix whose elements are the squares of the sums of their indices. | |
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Array[Plus[##]^2 &, {3, 3}]
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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  . | |
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NestList[ D[#, x]&, x^n, 3 ]
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