Can anybody help me on this exercise? I have to find the power series of the following function in zero.
$f(z) = (z^2 +4)^{-1}$
Can I use the Taylor formula?! Because then $f^{(n)}(0)$ will be zero for all $n>0$ but this does not look right to me :/
Would be nice if someone could give me a hint.
As $z^2 \to 0$, one may use the standard geometric result, $$ f(z)=\frac1{z^2+4}=\frac14\cdot\frac1{1+\frac{z^2}4}=\sum_{n=0}^\infty(-1)^n\frac{z^{2n}}{4^{n+1}}. $$