Thread: why this point is not essential singular point

if we go f(z)=+infinity
if we go f(z)=-infinity
we dont have a limit here
so why its a pole
??
by my definition a pole is when
if g is analitical at g(a) then 'a' in th n'th order pole
but in my case there is no (a-z)^n representation
and i proved that there is no limit

in my exam i have much complicated functions
and i cant develop it into a series every time

i tried to solve this one strictly by the limit tests
where am i wrong in my limit test
where is my conclusion wrong
??

Originally Posted by transgalactic

if we go f(z)=+infinity
if we go f(z)=-infinity
we dont have a limit here
so why its a pole
??
by my definition a pole is when
if g is analitical at g(a) then 'a' in th n'th order pole
but in my case there is no (a-z)^n representation
and i proved that there is no limit

in my exam i have much complicated functions
and i cant develop it into a series every time

i tried to solve this one strictly by the limit tests
where am i wrong in my limit test
where is my conclusion wrong
??

If has a zero of order at then has a pole of order at . Now use this with . Note however that the function does have an essential singularity at . Another thing, your argument is wrong since there is no or when dealing with complex functions (only a single point ).

thanks