# Making a list with a function: makelist

### 5.40.2 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 5.15.1).
  - 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 | ⎤ ⎦