# Thread: Taylor and Maclaurin Series

1. ## Taylor and Maclaurin Series

hi im having abit of trouble with taylor series at the moment

i understand the concept and can easily find a taylor series of a function to degree 3 or 4, however this semester im dealing with infinte complex series and forming a taylor series of a complex function.

for example:

Find the power series about the origin for (z^2)cos(z)

i was wandering if there is an easier way to determine this without finding the first few derivatives and trying to figure out the series from what values we ontain.

if someone could give some tips or somewhere where i could find some worked examples of this it would really help me out.

Many Thanks

2. Originally Posted by Reece
hi im having abit of trouble with taylor series at the moment

i understand the concept and can easily find a taylor series of a function to degree 3 or 4, however this semester im dealing with infinte complex series and forming a taylor series of a complex function.

for example:

Find the power series about the origin for (z^2)cos(z)

i was wandering if there is an easier way to determine this without finding the first few derivatives and trying to figure out the series from what values we ontain.

if someone could give some tips or somewhere where i could find some worked examples of this it would really help me out.

Many Thanks
You should know that

$\displaystyle \cos(z)=\sum_{n=0}^{\infty}\frac{(-1)^nz^{2n}}{(2n)!}$

$\displaystyle \Rightarrow{z^2\cos(z)}=z^2\cdot\sum_{n=0}^{\infty }\frac{(-1)^nz^{2n}}{(2n)!}=\sum_{n=0}^{\infty}\frac{(-1)^nz^{2n+2}}{(2n)!}$