a is 0 r>0 but i don't understand where M comes in exactly. how does this show that f''(0)=0=f'''(0) and so on
in addition do i show (b) and (c)?
i need this asap
g(z) is also analytic so it too achieves its maximum on the boundary which would mean that g(z) is less than or equal to 1 inside as well which proves that |f(z)| is less than or equal to |e^z| inside... I'm not sure if this is correct, but i feel like I'm on the right track
for n=0 should it be 5z^3 not 5z^2? and just to make sure,
when n=1 it would be the integral of 1/z+3+5z^2 which would be 2pi(i)
and n=2 integral of 1/z^2+3/z+5z which would be 6pi(i)
and n=3 again would be 0
n=4 would be 10pi(i)
so the possilbe values are 0,2pi(i), 6pi(i) and...
Homework Statement
Let f(z) be an entire function such that |f(z)| less that or equal to R whenever R>0 and |z|=R.
(a)Show that f''(0)=0=f'''(0)=f''''(0)=...
(b)Show that f(0)=0.
(c) Give two examples of such a function f.
Homework Equations
The Attempt at a Solution...