- #1
matheater
- 7
- 0
I have the following problems
(1)Consider the series ∑z^n,|z|<1 z is in C
I thik this series is absolutely and uniformly comvergent since the series ∑|z|^n is con vergent for |z|<1,but I have a book saying that it is absolutely convergent,not uniformly...i am confused...
(2)for the function f(z)=1/√(z-1),z=1 is a (a)pole (b)an essential singularity ?
I think it is an essential singularity since if it is a pole,say of order m then m is a positive integer and we can write f(z)=g(z)/(z-1)^m, where g(z) is analytic at z=1 and g(1)≠0,
but the given function cannot be written in this way,but the answer is given pole,i am again confused...
Can anybody help me?
(1)Consider the series ∑z^n,|z|<1 z is in C
I thik this series is absolutely and uniformly comvergent since the series ∑|z|^n is con vergent for |z|<1,but I have a book saying that it is absolutely convergent,not uniformly...i am confused...
(2)for the function f(z)=1/√(z-1),z=1 is a (a)pole (b)an essential singularity ?
I think it is an essential singularity since if it is a pole,say of order m then m is a positive integer and we can write f(z)=g(z)/(z-1)^m, where g(z) is analytic at z=1 and g(1)≠0,
but the given function cannot be written in this way,but the answer is given pole,i am again confused...
Can anybody help me?