Suppose that is an entire functionand that there are positive constants and with if . Show that is a polynomial of degree or less.
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Originally Posted by chiph588@ Suppose that is an entire functionand that there are positive constants and with if . Show that is a polynomial of degree or less. isn't this just a slight twist on the (extended) Liouville's theorem?
Originally Posted by chiph588@ Suppose that is an entire functionand that there are positive constants and with if . Show that is a polynomial of degree or less. Let . If is an entire function then and . If on then By hypothesis for . Therefore, if then on we have Thus, . Thus, if then by making sufficiently large we have . Thus, is a polynomial of degree at most .
That's the proof I used, does that prove it for the disk also?
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