Suppose that we have n-th degree polynomial p(x)=a0+a1(x−a)+a2(x−a)2+…+an−1(x−a)n−1+an(x−a)n, where a,a0,a1,a2,…,an are constants.
When a=0 we call Taylor polynomial Maclaurin polynomial. In this case formulas for polynomials are fairly simple.
Maclaurin Polynomial. For function y=f(x) Maclaurin polynomial of n-th degree is Mn(x)=f(0)+1!f′(0)x+2!f′′(0)x2+…+n!f(n)(0)xn.