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**[SOLVED] Laurent Series of z/(sin z)^2**

**Homework Statement**

Find the first four terms of the Laurent series of [itex]f(z) = z/(\sin z)^2[/itex] about 0.

**The attempt at a solution**

I know that when z = 0, f(z) is undefined so it has a singularity there. This singularity is a pole because

[tex]\lim_{z \to 0} \left|\frac{z}{(\sin z)^2}\right| = \infty[/tex]

I want to find the order of this pole, which according to my book is the order of the zero z = 0 of 1/f(z). But z = 0 is not a zero of 1/f(z) because it is undefined at z = 0.

My plan of attack is to find the order of the pole z = 0, find the form of the Laurent series of f, expand [itex]f(z)(\sin z)^2[/itex], equate it to z and get the first four terms of the Laurent series.