# Building Lists from Functions

Array[f,n] | generate a length n list of the form |

Array[f,{n_{1},n_{2},...}] | 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[{f_{1},f_{2},...},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.

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This produces a list whose elements are

.

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This generates a 2×3 matrix whose entries are

.

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This generates a 3×3 matrix whose elements are the squares of the sums of their indices.

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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

.

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