Citizendium - a community developing a quality, comprehensive compendium of knowledge, online and free.
Click here to join and contribute
CZ thanks our previous donors. Donate here. Treasurer's Financial Report


From Citizendium
Jump to: navigation, search
This article is developing and not approved.
Main Article
Related Articles  [?]
Bibliography  [?]
External Links  [?]
Citable Version  [?]
To learn how to update the categories for this article, see here. To update categories, edit the metadata template.
 Definition For given function , solution of equation [d] [e]
Checklist and Archives
 Workgroup category Mathematics [Please add or review categories]
 Talk Archive none  English language variant Not specified

Superfunction evaluated *at point t*

I seem to not to become familiar with the concept of Superfunctions. But I understand now at least one reason. If we say "F(z) = f(f(f(...f(t))), where f is evaluated z times" then we obscure, that we evaluate f initially *at the point t*. That means, for each *t* we have another superfunction! So a) we should notice that in the article (I couldn't make the change, don't know why) and b) should change the notation, to something like "F_t(z) = f(f(f(...f(t))), where f is evaluated z times beginning at t".

We'll see then, that the range of the "superfunction at some t" is limited to intervals around t between fixpoints and that "F_t(z)" cannot exceed that intervals by change of the parameter z (as long as z is real, there is one option for complex z to step to a neighboured interval). An example is "f(t)=2^t-1 ", whose superfunction -if evaluated beginning at any value "0<t<1" - cannot exceed this range.

--Gottfried Helms 06:50, 24 November 2011 (UTC)