Find laurent series expansion

1. How do you find the Laurent series expansion?
2. How do you find the principal part of Laurent expansion?
3. How do you find the Laurent coefficient?
4. How do you find the region of convergence in Laurent series?

How do you find the Laurent series expansion?

Determine the Laurent series for the function, f(z) = (z+1)/z around z₀ = 0. Also, define the region where the function is valid. Hence, f(z) = 1+ (1/z) is the Laurent series, which is valid on the infinite region 0 < |z| < ∞.

How do you find the principal part of Laurent expansion?

The portion of the series with negative powers of is called the principal part of the expansion. It is important to realize that if a function has several ingularities at different distances from the expansion point , there will be several annular regions, each with its own Laurent expansion about .

How do you find the Laurent coefficient?

c−1=12πi∮γf(t)dt.

How do you find the region of convergence in Laurent series?

Its radius of convergence around z=−2, and therefore the radius of convergence of your Laurent series, is simply the distance from −2 to the nearest non-differentiable point, i.e. z=−1.