- #1

Volt

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- 0

## Homework Statement

Find the Laurent series expansion of f(z) = (e^z - 1) / (sinz)^3 at z = 0.

## The Attempt at a Solution

Ok, so I'm confused on a number of fronts here. For e^z - 1, I assume you just use the standard power series expansion of e^z and then tack on a -1 at the end, which would give you the Taylor series of that part.

For 1/(sinz)^3 though, I'm really confused. I'm not even sure about (sinz)^3, nevermind the inverse. Do you take the power series of sinz multiplied three times to get (sinz)^3 and then somehow inverse it? I mean, nevermind the Laurent series, I'm not even sure what the Taylor series of (sinz)^3 is. I guess you could try to find a formula for the nth derivative and then use that formula for the Taylor series, but that looks like it would be pretty messy or even impossible. I'm sure I'm missing something obvious here but I don't know what.