# Taylor Series Expansion

## Homework Statement

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

## 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:

## Answers and Replies

Dick
Science Advisor
Homework Helper
They are exactly the same thing. The first expression is just the first two terms of the second.

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

Dick
Science Advisor
Homework Helper
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

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.

ah right. Thanks for pointing that out.