Borel summation

Borel summation is a mathematical technique used to assign meaningful sums to certain divergent series—series whose terms grow too quickly for traditional addition to work. It involves transforming the original series into a new function (via the Borel transform), which often converges, then integrating this function to produce a finite value. This process effectively "resums" the divergent series, providing a way to interpret and work with them in mathematical and physical contexts where naive summation fails. It’s a powerful tool for extending the concept of summation beyond finite or convergent series.