Q. Let f be a function which is differentiable and suppose that the function satisfies :
Then show f is identically equal to zero.
I know I probably need to use Liouville's Theorem here, but I don't know how to go about it. Any help would be appreciated. Thanks.
It follows from the Extended Liouville's theorem (you may know it under a different name )
Basically, it says if is an entire function and
then is a polynomial of degree at most
here is an integer and and are constants (positive constants if memory serves me correctly)
note that the case k = 0 is the original Liouville's theorem