- #1
krindik
- 65
- 1
Hi,
can u pls help me on this?
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]
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
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