tommy beta method - 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: tommy beta method (/showthread.php?tid=1372) tommy beta method - tommy1729 - 12/09/2021 Consider the following (double) integral where h is a positive infinitesimal $B(s)=\int_h^s \int_h^\infty \frac{cos(zt)dtdz}{t^t}$ This integral is intended as an analogue for erf(s) but which is suppose to go - C for Re(s) << -1 and + C for Re(s) >> 1 ( independant of the imaginary part ! ). Where C is a (probably nonzero and positive ) real constant. Assuming that indeed 0 < C we continue :   $tb(s)=\frac{1+\frac{B(s)}{C}}{2}$ Now consider  $f(s)=\exp(tb(s) f(s-1))$ And finally we get lim n to +oo ; $tet_{tb}(s)=ln^{[n]}f(s+n)$ I call it tommy beta method , hence "tb" This ofcourse requires more research. regards tommy1729 Tom Marcel Raes