Timeline for "Closed-form" functions with half-exponential growth
Current License: CC BY-SA 2.5
7 events
| when toggle format | what | by | license | comment | |
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| Apr 29, 2011 at 18:00 | comment | added | John Sidles | The analytic structure of the Lambert W function points to an even stronger conjecture: for values d>e^(1/e), no smooth function satisfies the composition f(f(n))=d^n. It's no wonder that these demi-exponential functions (as Dick Lipton and Ken Regan call them) have earned a reputation for being difficult to construct. | |
| Nov 9, 2010 at 21:23 | vote | accept | Scott Aaronson | ||
| Nov 9, 2010 at 21:22 | comment | added | Scott Aaronson | Thanks so much, Gerald! Yeah, I also made the observation that every montone composition of *, +, exp, log has an integer-valued "exponentiality level" associated with it. But I didn't know how to prove that this "level property" is preserved under subtraction and division. I'll take a look at the references you gave! | |
| Nov 9, 2010 at 19:48 | comment | added | Gerald Edgar | When Scott reads this, he may think of adding inverse function to his operations. That may get you outside of the original Hardy space, but still keeps you within the transseries. | |
| Nov 9, 2010 at 19:39 | history | edited | Gerald Edgar | CC BY-SA 2.5 |
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| Nov 9, 2010 at 19:33 | comment | added | Thierry Zell | Indeed, I think that you don't even need to get into transseries per se; looking at the Hardy field should be enough, so that looking at older references like Rosenlicht's papers might be enough to prove it. See e.g. jstor.org/stable/1999639 | |
| Nov 9, 2010 at 19:30 | history | answered | Gerald Edgar | CC BY-SA 2.5 |