Nachbin's Theorem - Nachbin Resummation

Nachbin Resummation

Nachbin resummation (generalized Borel transform) can be used to sum divergent series that escape to the usual Borel resummation or even to solve (asymptotically) integral equations of the form:

where f(t) may or may not be of exponential growth and the kernel K(u) has a Mellin transform. The solution, pointed out by L. Nachbin himself, can be obtained as with and M(n) is the Mellin transform of K(u).