Taylor or Maclaurin Series

Many functions can be written as powers series about some point of their domain. About the origin this gives

f(x) = f(0) + f'(0)x/1! + f''(0)x2/2! + f'''(0)x3/3! + ...
and is called the Maclaurin series of f.

About a different point a (say) we get

f(a + h) = f(a) + f'(a)h/1! + f''(a)h2/2! + f'''(a)h3/3! + ...
which we call the Taylor series of f.