tommy beta method - Printable Version

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tommy beta method - Printable Version

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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