12/09/2021, 11:48 PM
Consider the following (double) integral where h is a positive infinitesimal
=\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 :
=\frac{1+\frac{B(s)}{C}}{2})
Now consider
=\exp(tb(s) f(s-1)) )
And finally we get lim n to +oo ;
=ln^{[n]}f(s+n))
I call it tommy beta method , hence "tb"
This ofcourse requires more research.
regards
tommy1729
Tom Marcel Raes
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.
regards
tommy1729
Tom Marcel Raes
