Borel, then an unknown young man, discovered that his summation method gave the 'right' answer for many classical divergent series. He decided to make...
22 KB (3,525 words) - 19:07, 1 October 2024
Divergent series (redirect from Summation method)
with explicit and natural techniques such as Abel summation, Cesàro summation and Borel summation, and their relationships. The advent of Wiener's tauberian...
32 KB (5,028 words) - 01:29, 5 August 2024
Nachbin's theorem (redirect from Generalized Borel transform)
to give the domain of convergence of the generalized Borel transform, also called Nachbin summation. This article provides a brief review of growth rates...
7 KB (1,308 words) - 00:39, 3 October 2024
results in the renormalization of quantum field theories. Borel summation Cesàro summation Divergent series Ramanujan's sum Abel–Plana formula Bruce C...
7 KB (1,364 words) - 10:12, 29 August 2024
same. Abel summation Abel's summation formula Abel–Plana formula Abelian and tauberian theorems Almost convergent sequence Borel summation Divergent series...
9 KB (1,504 words) - 19:44, 15 October 2024
divergent, it can be assigned a value of approximately 0.596347 by Borel summation. This series was first considered by Euler, who applied summability...
5 KB (686 words) - 18:55, 28 March 2024
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...
4 KB (750 words) - 19:35, 24 December 2022
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...
13 KB (1,209 words) - 07:48, 21 August 2024
1 − 2 + 4 − 8 + ⋯ (section Borel summation)
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...
9 KB (1,143 words) - 23:34, 16 October 2024
1 + 2 + 3 + 4 + ⋯ (section Ramanujan summation)
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...
33 KB (4,228 words) - 05:02, 24 September 2024