This is bief and easy to understand.....

2. Published by
Muhammad Umer
15103122-017
Electrical Engineer
University Of Gujrat
Pakistan

3. Topic
Laurent series

4. The Laurent series is a representation of a
complex function f(z) as a series. Unlike
the Taylor series which expresses f(z) as a
series of terms with non-negative powers
of z, a Laurent series includes terms with
negative powers.

5.  In mathematics, the Laurent series of a
complex function f(z) is a representation of
that function as a power series which includes
terms of negative degree. It may be used to
express complex functions in cases where
a Taylor series expansion cannot be applied.

6. To calculate the Laurent series
we use the standard and
modified geometric series
which are

8.  Here f(z) = 1 where z is
analytic everywhere apart
from the singularity at z = 1.
Above are the expansions for
f in the regions inside and
outside the circle of radius 1,
centred on z = 0, where z < 1
is the region inside the circle
and z > 1 is the region
outside the circle.

9. Masnsoor kashif 15103122-024

10. Determine the Laurent series for

13.  Mehmood ul hassan 15103122-022

16.  Wasif uz zaman 15103122-021

17. Example

18.  Expand by using Laurent series

23.  Shoaib 15103122-002

24. Example