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Tetration Extension to Real Heights
#1
I saw the wiki page that mentioned extending tetration to real heights...
<http://en.wikipedia.org/wiki/Tetration#Extension_to_real_heights>

That would be a↑↑x for x∈R and a=constant. I was wondering if anyone knew the names of any books or papers that went over the process of this extension
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#2
I think the method you are refering to is what we call natural or intuitive tetration. If you would like a terse intro then google Peter Walker on scholar.google.com However, if you would like an easier discussion then you can read my paper which I need to put back online...

Also I believe Henryk gave a nice intro to the above method somewhere on this site...

If you are feeling really adventurous then you can search this forum for Jay Fox and see his improvement to speed and accuracy of the above method.

Andrew Robbins
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#3
Thanks,

Peter Walkers paper seems to be what I need. I'll also be interested in reading your paper when you get around to putting it back up
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#4
(05/10/2010, 06:16 PM)chobe Wrote: I saw the wiki page that mentioned extending tetration to real heights...
<http://en.wikipedia.org/wiki/Tetration#Extension_to_real_heights>

That would be a↑↑x for x∈R and a=constant. I was wondering if anyone knew the names of any books or papers that went over the process of this extension

There is also a (unfortunately unfinished) survey paper explaining the different methods in detail here. However most of the methods except regular iteration are not yet proven to be valid. Despite, numerical evidence supports that these are working well.
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