Web pages for infinitely iterated exponentials

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Dave L. Renfro

Jul 23, 2001, 2:47:48 PM7/23/01
This is a list of web pages involving the convergence of x^x^x...
that I wanted to archived at sci.math for something I'm working on.
Also, since this topic comes up fairly often in sci.math, the
archived-URL for this post can be used to quickly disseminate a
lot of information to newbies asking questions on this topic.

1. "Iterated Exponential Constants" at Steven Finch's "Favorite
Mathematical Constants" web page. [Some nice graphs along with 26
references. Has a 7 page Netscape Print Preview output.]


2. Ioannis Galidakis's "Infinite Exponentials" and "A slightly
deeper analysis". [These have 9 and 11 page Netscape Print
Preview outputs, respectively.]


3. Joseph MacDonnell's "Some Critical Points of the Hyperpower
Function y = x^x^x^..." [Has a 7 page Netscape Print Preview


4. Louis A. Talman's "On x^x^x..." [Click on 'For what real x does
the "continued exponential" x^(x^(x^(x^...)))'. 464K .pdf,
19K .dvi, and 79K .ps files available. The .ps file generates a
5 page output.]


5. This web page gives what appears to be a paradox involving the
equation x^(x^(x^(...))) = 2.


6. John Bailey's "What is i^i^i^i...." [Gives 15 links to math
discussion posts on this topic. See also item #13 below.]


7. Two sci.math threads "Hyper-Exponentiation" [7 posts, April 23
to 24, 1999; 5 posts, Oct. 22 to 31, 1999.]


8. sci.math: "Problems in (0,1/e)" [Dave L. Renfro post dated
Sept. 9, 1999. Has a 2 page Netscape Print Preview output.]


9. sci.math thread "x^x^x^x^x^..." [15 posts, Oct. 1 to 10, 1999.]


10. sci.math thread "Interpolation of iterated exponentiation?"
[3 posts, all Nov. 16, 1999.]


11. sci.math.research thread "polypowers/iterated exponentials"
[3 posts, Dec. 22 to 26, 1999.]


12. sci.math thread "z^z^z^...". [15 posts, March 21 to 23, 2000.]


13. sci.math thread "i^i^i^..." [6 posts, March 23 to 24, 2000. See
also item #6 above.]


14. sci.math thread "rankings of x^y^z^..." [6 posts, April 11 to
13, 2000.]


15. Two sci.math threads "x^x^x^..." [5 posts, Sept. 9 to 15, 1996;
16 posts June 20 to July 3, 2001.]


Dave L. Renfro

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