The topic can be complex, but I am interested in the technique of heat kernel for the regularization of a divergent series at a specific point b=0. I mean, if one already knew a convergent series for each point b (being b different to zero where the series diverges), can I transform the divergent series at b=0 in a convergent series at b=0 by the heat kernel regularization or another technique to try to approach the series at the divergent point b=0? I see only the heat kernel or zeta function regularization as potential candidates for fixing divergent series when a specific value b is studied.

Let me know PDFs or links about the regularization from convergent series that diverges at b=0. Particularly I am interested in what has been exposed in this link: https://math.stackexchange.com/questions/1964838/equivalence-of-regularization-schemes-of-divergent-series/4597704#4597704

As the approach seems to be very interesting.

Best regards

Carlos L.