Menu Close

how-can-find-taylor-series-of-f-z-cot-z-when-z-5pi-




Question Number 147417 by tabata last updated on 20/Jul/21
how can find taylor series of f(z)=cot(z) when z=5π
$${how}\:{can}\:{find}\:{taylor}\:{series}\:{of}\:{f}\left({z}\right)={cot}\left({z}\right)\:{when}\:{z}=\mathrm{5}\pi \\ $$
Answered by mathmax by abdo last updated on 21/Jul/21
f(z)=Σ_(n=0) ^∞  ((f^((n)) (5π))/(n!))(z−5π)^n   f(z)=(1/(tanz)) ⇒f(5π)is not defined..!
$$\mathrm{f}\left(\mathrm{z}\right)=\sum_{\mathrm{n}=\mathrm{0}} ^{\infty} \:\frac{\mathrm{f}^{\left(\mathrm{n}\right)} \left(\mathrm{5}\pi\right)}{\mathrm{n}!}\left(\mathrm{z}−\mathrm{5}\pi\right)^{\mathrm{n}} \\ $$$$\mathrm{f}\left(\mathrm{z}\right)=\frac{\mathrm{1}}{\mathrm{tanz}}\:\Rightarrow\mathrm{f}\left(\mathrm{5}\pi\right)\mathrm{is}\:\mathrm{not}\:\mathrm{defined}..! \\ $$

Leave a Reply

Your email address will not be published. Required fields are marked *