6.40.2  Making a list with a function: makelist

The makelist command creates lists built from values of a function.

• makelist takes three mandatory arguments and one optional argument:
  • f, a function (see Section 6.15.1).
  • a and b, two real numbers.
  • Optionally p, a step size (by default 1 if b>a and −1 if b < a).
• makelist(f,a,b ⟨,p⟩) returns the list [f(a),f(a+p),…,f(a+k p)] with k such that: a<a+k p ≤ b <a+(k+1) p or a>a+k p ≥ b >a+(k+1) p.

Examples.
(In these examples, purge x if x is not symbolic.)

• Input:
  makelist(x->x^2,3,5)
  or:
  makelist(x->x^2,3,5,1)
  or: Input:

  h(x):=x^2

  makelist(h,3,5,1)

  Output:

  ⎡ ⎣

  9,16,25

  ⎤ ⎦

• Input:
  makelist(x->x^2,3,6,2)
  Output:

  ⎡ ⎣

  9,25

  ⎤ ⎦

• Input:
  makelist(4,1,3)
  regards 4 as the constant function, and so creates a list with entries 4, from integers 1 to 3. This is the same as [4 $ 3].
  Output:

  ⎡ ⎣

  4,4,4

  ⎤ ⎦