Laurent expansion of rational function
The Laurent series expansion of a rational function may often be determined using the uniqueness of Laurent series coefficients in an annulus and applying geometric series. We will determine the expansion of
by the powers of .
We first have the partial fraction decomposition
whence the principal part of the Laurent expansion contains . Taking into account the poles of we see that there are two possible annuli for the Laurent expansion:
a) The annulus . We can write
b) The annulus . Now we write
This latter Laurent expansion consists of negative powers only, but isn’t an essential singularity of , though.
|Title||Laurent expansion of rational function|
|Date of creation||2013-03-11 19:16:06|
|Last modified on||2013-03-11 19:16:06|
|Last modified by||(0)|