## 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)*x*^{2}/2! + *f*'''(0)*x*^{3}/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*)*h*^{2}/2! + *f*'''(*a*)*h*^{3}/3! + ...

which we call the **Taylor series** of *f*.