- #1

krindik

- 65

- 1

can u pls help me on this?

## Homework Statement

Find Laurent series that converges for

[tex]

\, 0 < |z - z_0| < R }

[/tex] and determine precise region of convergance

[tex]

\, \frac {1}{z^2 + 1} \,\,

[/tex]

## Homework Equations

## The Attempt at a Solution

I tried to spilt this into fractions

i.e

[tex]

f(x) \, = \, \frac{A}{z-i} + \, \frac{B}{z+i}

[/tex]

as I would have done for

[tex]

\frac {1}{z^2 - 1} \,\,

[/tex]

But in that case I would expand it with a geometrical series.

The problem rises with [tex] i [/tex] instead of [tex] 1 [/tex]

**2. Homework Statement**

Can u pls explain how can I choose the method of expansion (Laurent, Taylor) given a function f(x) ?

Thanks