Sexp redefined ? Exp^[a]( - 00 ). + question ( TPID 19 ??) - Printable Version +- Tetration Forum ( https://math.eretrandre.org/tetrationforum)+-- Forum: Tetration and Related Topics ( https://math.eretrandre.org/tetrationforum/forumdisplay.php?fid=1)+--- Forum: Mathematical and General Discussion ( https://math.eretrandre.org/tetrationforum/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 |