In mathematics, a Taylor series is a representation of a function as an infinite sum of terms. A few examples are given below. e^x = sigma^infinity _n = 0 x^n! = 1 + x + x^2/2! + x^3/3! + ... for all x sin x = sigma^infinity _n = 0 (-1)^n/(2n + 1)! x^2n + 1 = x - x^3/3! + x^5/5! - ... for all x cos x = sigma^infinity _n = 0 (-1)^n/(2n)! x^2n = 1 - x^2/2! + x^4/4! - ... for all x tan x = sigma^infinity _n = 1 B_2n (-4)^n (1 - 4^n)/(2n)! x^2n - 1 = x + x^3/3 + 2x^5/15 + ... for |x|