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Topic: Analytic solutions for f(ax)=(f(x))^2+b
Replies: 36   Last Post: Mar 13, 2009 5:51 AM

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 matt271829-news@yahoo.co.uk Posts: 2,136 Registered: 1/25/05
Re: Analytic solutions for f(ax)=(f(x))^2+b
Posted: Jan 22, 2009 9:51 AM

On Jan 22, 11:37 am, David C. Ullrich <dullr...@sprynet.com> wrote:
> On Wed, 21 Jan 2009 14:48:10 EST, amy666 <tommy1...@hotmail.com>
> wrote:
>

> >btw all "math" on denis website is actually stolen and copied from others.
>
> >tell me something , if c = positive real and
>
> >f(ax)=(f(x))^2+b
>
> >then what is
>
> >f(a^c x) = ??
>
> Why in the world do you imagine that f(ax)=(f(x))^2+b
> implies anything about f(a^c x) (when c is not an integer)?
>
> Supposing it did imply something about that, why would
> you imagine that this has something to do with continuuous
> iteration?

The connection with continuous iteration is like this...

Assume f(1) = k and define g(x) = x^2 + b, then

f(a^n) = g^n(k)

So

f(x) = g^(log(x)/log(a))(k)

So if we can find an expression for g^n(x) for arbitrary real n then
we have a solution for f(x).

Date Subject Author
1/21/09 Denis Feldmann
1/21/09 amy666
1/21/09 Denis Feldmann
1/21/09 amy666
1/21/09 amy666
1/21/09 Denis Feldmann
1/21/09 Denis Feldmann
1/22/09 amy666
1/22/09 Denis Feldmann
1/22/09 amy666
1/22/09 amy666
1/23/09 Denis Feldmann
1/22/09 David C. Ullrich
1/21/09 Denis Feldmann
1/21/09 amy666
1/21/09 Denis Feldmann
1/22/09 amy666
1/22/09 David C. Ullrich
1/22/09 amy666
1/22/09 David C. Ullrich
1/22/09 amy666
1/23/09 David C. Ullrich
1/22/09 matt271829-news@yahoo.co.uk
1/22/09 alainverghote@gmail.com
1/22/09 David C. Ullrich
1/22/09 amy666
1/23/09 lwalke3@lausd.net
1/23/09 Denis Feldmann
3/12/09 mike3
3/12/09 mike3
3/13/09 alainverghote@gmail.com
1/22/09 David C. Ullrich
1/21/09 matt271829-news@yahoo.co.uk
1/21/09 matt271829-news@yahoo.co.uk
1/22/09 alainverghote@gmail.com
1/22/09 alainverghote@gmail.com
3/7/09 mike3