Taylor series for the cosine function in Lisp

Question

I'm trying to build a Taylor series in lisp, as the following image.

1 + x^1/1! + x^2/2! + x^3/3!.....etc

the power and factorial functions are already implemented in order to use them in taylor function.

currently i wrote the following initial code to solve the equation.

(defun taylor(x n)
(if (= n 0) 1
(+ (/ (power x n) (factorial n)) (taylor(x (- n 1))))))

using this code will cause the following error

error: unbound function - X

---

im new in lisp, so any help will be appreciated :D

Answer 1

You have an extra parenthesis in front of taylor; i.e. you need to call it as (taylor x n) and not (taylor (x n)).

In general, errors like these are much easier to spot if you indent code appropriately, e.g. the following

(defun factorial (n)
    (if (= n 1)
        1
        (* n (factorial (1- n)))))

(defun power (x n)
    (if (= n 1)
        x
        (* x (power x (1- n)))))

(defun taylor (x n)
    (if (= n 0)
        1
        (+ (/ (power x n)
              (factorial n))
           (taylor x (- n 1)))))