 Welcome back MechanicalEI. Did you know that a Taylor series is a representation of a function as an infinite sum of terms that are calculated from the values of the function's derivatives at a single point and that a Lorentz series of a complex function f of z is a representation of that function as a power series which includes terms of negative degree? This makes us wonder, what are Taylor's and Lorentz series? Before we jump in, check out the previous part of this series to learn about what properties of line integral are. Now, the Taylor series of a real or complex valued function f of x that is infinitely differentiable at a real or complex number a is the power series which can be written in the more compact sigma notation as summation of f power n of a upon n factorial into x minus a the whole raised to n from n equals to 0 to infinity. Here, f power n of a denotes the nth derivative of f evaluated at a. The Lorentz series of a complex function f of z is a representation of that function as a power series which includes terms of negative degree. It may be used to express complex functions in cases where a Taylor series expansion cannot be applied. The Lorentz series for a complex function f of z about a point c is given by f of z equals to summation of a n into z minus c raised to n from n equals to minus infinity to infinity where a n and c are constants defined by a line integral which is a generalization of Cauchy's integral formula. Hence, we first saw what Taylor's series is and then went on to see what Lorentz series is. So like, subscribe and comment with your feedback to help us make better videos. Thanks for watching. Also, thanks a lot for those constructive comments. You helped the channel grow. So here are the top mechanical EIs of our last videos. In the next episode of Mechanical EI, find out what residue theorem is.