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Consider the following (double) integral where h is a positive infinitesimal

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 :

Now consider 

And finally we get lim n to +oo ;

I call it tommy beta method , hence "tb"

This ofcourse requires more research.



Tom Marcel Raes