# Homework Help: Taylor Series Expansion

1. Oct 27, 2011

### Applejacks

1. The problem statement, all variables and given/known data

Find the Taylor series expansions for f(z) = −1/z^2 about z = i + 1.

2. Relevant equations

3. The attempt at a solution

I'm just not sure what format I'm supposed to leave it in.

Is it meant too look like this:
f(z)=f(i+1)+f'(i+1)(x-i-1)...

or this
Ʃ$\frac{1}{n!}$$f^{(n)}$(1+i) * (z-i-1)^n (also is this correct?)

Last edited: Oct 27, 2011
2. Oct 27, 2011

### Dick

They are exactly the same thing. The first expression is just the first two terms of the second.

3. Oct 27, 2011

### Applejacks

Yeah I'm aware of that. I guess I should keep it in the second form though. Another question: what does the square do to the function. What I wrote can't be correct because -1/z would give the same thing.

Ʃ$\frac{1}{n!}$$f^{(n)}$(1+i) * (z-i-1)^2n

4. Oct 27, 2011

### Dick

What?? Changing f changes f^(n)(i+1). That changes the series doesn't it? The power part (z-i-1)^n doesn't change. Those are the powers in the expansion of any function around i+1.

5. Oct 27, 2011

### Applejacks

ah right. Thanks for pointing that out.