Re: analytic function... need help.

On 25 Nov 2005 15:18:33 -0800, curtispro@xxxxxxxxx wrote:

>suppose that f is analytic on the disk |z|<=1. Show that there is a
>positive integer n such that f(1/n) =/= 1/(n+1).

This doesn't make much sense as a post to sci.logic -
sci.math would be better.

Anyway, let g(z) = 1/f(1/z). Then f(1/n) = 1/(n+1)
says

(*) g(?) = ??.

Now when you figure out what (*) is there is an
obvious function g_0 that satisfies (*). This
gives you a function f_0 that satisfies f_0(1/n)
= 1/(n+1). But it turns out f_0 is not analytic
in the closed unit disk.

Now, there is at most one analytic function
f satisfying f(1/n) = 1/(n+1), because ____.
Hence that fact that f_0 doesn't work shows
that there is no solution.

>Need help.


************************

David C. Ullrich
.

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