Re: help required

From: Stuart M Newberger (smnewberger_at_comcast.net)
Date: 03/03/05 

Date: 3 Mar 2005 00:49:40 -0800

nonton wrote:
> I am trying to show:
>
> Suppose k is a path, the point function h is continuous on K' i.e.
the
> carrier of K, and f is a sequence such that, for each nonnegative
> integer n, f_n is the point function to which {a,b} belongs only in
> case a is a point not in K' and
>
> b= n! intergral of h/ (I+a)^n+1 with respect to the path K.
>
> If n is a nonnegative integer then f'_n= f_n+1
>
> Thank you.
>
> I looked at when n=o and n=1
>
> I found out that as p approaches q , f'_0(q) is the same as n=1 when
i
> use the difference quotient.
>
> I know that f_o= integral h/(I-a) w.r.t. the path K.
>
> How do I go about this please.

A proof by induction on n can be found in Ahlfors,Lars V.,Complex
Analysis in chapter 4 (pg 121 of 2nd edition but around there in the
3rd edition).It is a special case case of the Leibnitz rule for
differentiation under the integral sign.Regards,Stuart M Newberger