Re: Help Needed

On Jan 16, 1:53 pm, William Elliot <ma...@xxxxxxxxxxxxxxxxxx> wrote:
On Wed, 16 Jan 2008, carkaci wrote:
I have a following recurrence relation

y_0 = f ( x )
y_1 = f ( y_0 )
y_2 = f ( y_1 )
..
..
y_n= f ( y_(n-1) )

where n is +inf.

I know that y_n = sin(x), how can I find f(x) ?

Restatement?
        If lim(n->oo) f^n(x) = sin x, what is f(x)?

There is not such f.

sin f(x) = lim(n->oo) f^n(f(x)) = lim(n->oo) f^(n+1)(x)
        = lim(n->oo) f^n(x) = sin x

some k in Z with f(x) = 2.pi.k + x

lim(n->oo) f^n(x) = oo if, 0 < k
                = x, if k = 0
                = -oo, if k < 0

----
By the way n is not a power of function.
Restatament : f( f( f( f( f( f( f( f( .....f(x).....) ))))))) = sin(x)
I am looking for function f?





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