+- Tetration Forum (https://tetrationforum.org)
+-- Forum: Tetration and Related Topics (https://tetrationforum.org/forumdisplay.php?fid=1)
+--- Forum: Mathematical and General Discussion (https://tetrationforum.org/forumdisplay.php?fid=3)
+--- Thread: Sexp redefined ? Exp^[a]( - 00 ). + question ( TPID 19 ??) (/showthread.php?tid=1095)
Sexp redefined ? Exp^[a]( - 00 ). + question ( TPID 19 ??) - tommy1729 - 09/06/2016
I would like to say im not a huge fan of the usual definition used sexp(-2) = -oo.
So i use two new functions resp definitions that are just a " shift ".
Exp^[a](-00) = newsexp(a)
Now newsexp(0) = -00 and
Newslog(-00) = 0.
Exp^[a](x) is still newsexp(newslog(x) + a).
And newsexp is similar to ln , newslog is similar to exp.
-----
As Said in the title a ( returning ?) question that should perhaps be posted as TPID 19 in the open problems section.
Also clearly related to the above.
Consider all C^oo solutions to f(x) = exp[1/2](x).
Now consider the subset of those that satisfy
For all real x : f ' (x) , f " (x) > 0.
Then what are the max and min values of
f ( - oo ).
---
Although approximations exist , i am unaware of a good method , both in theory and numerical / practical.
No closed form known to me , not even with tet type functions.
If someone conjectured a closed form , i have no good method to consider proof or disproof ( only luck from iterations ).
It is pointless to add links to related subjects here , because almost all of them are !
So , therefore , I consider it a key question , perhaps worthy of a TPID 19.
----
Regards
Tommy1729