Borel, then an unknown young man, discovered that his summation method gave the 'right' answer for many classical divergent series. He decided to make...

with explicit and natural techniques such as Abel summation, Cesàro summation and Borel summation, and their relationships. The advent of Wiener's tauberian...

divergent, it can be assigned a value of approximately 0.596347 by Borel summation. This series was first considered by Euler, who applied summability...

same. Abel summation Abel's summation formula Abel–Plana formula Abelian and tauberian theorems Almost convergent sequence Borel summation Divergent series...

results in the renormalization of quantum field theories. Borel summation Cesàro summation Divergent series Ramanujan's sum Abel–Plana formula Bruce C...

theorem Borel right process Borel set Borel summation Borel distribution Borel's conjecture about strong measure zero sets (not to be confused with Borel conjecture...

Nachbin resummation (generalized Borel transform) can be used to sum divergent series that escape to the usual Borel summation or even to solve (asymptotically)...

usual formula. The Borel sum of 1 − 2 + 4 − 8 + ⋯ is also ⁠1/3⁠; when Émile Borel introduced the limit formulation of Borel summation in 1896, this was...

functions is identified as one of two broad classes of summation methods, including Abel and Borel summation, by Knopp, Konrad (1990) [1922]. Theory and Application...

of these methods are strictly weaker than Borel summation; for q > 0 they are incomparable with Abel summation. For some value y we may define the Euler...