Power series expansion

the power series expansion (or Taylor series expansion) of any continuous real mathematical function is the representation of it by an infinite series of power functions. In fact, any real continuous function can be written as

f(x) = Sanxⁿ, with n = 0,1,2,...

where S represents the sum sign and an is the coefficient for the power n. Finding the power series expansion for a specific function requires that the corresponding an are determined. For real functions the different a_n are found by taking the nth derivative of the function relative to x:

a_n = (dⁿf(x)/dxⁿ) taken at x = 0

Examples of power series expansions are given under exponential, trigonometric functions and velocity.