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 tommy beta method tommy1729 Ultimate Fellow Posts: 1,505 Threads: 358 Joined: Feb 2009 12/09/2021, 11:48 PM 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 « Next Oldest | Next Newest »

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