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...

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

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...

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...

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

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

In mathematics, Mittag-Leffler summation is any of several variations of the Borel summation method for summing possibly divergent formal power series...

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...

generalized Borel theory of summation, and applied this to study problems connected to convergence of complex power series. He defined new summation methods...

to give the domain of convergence of the generalized Borel transform, also called Nachbin summation. This article provides a brief review of growth rates...

In mathematics, Borel transform may refer to A transform used in Borel summation A generalization of this in Nachbin's theorem This disambiguation page...

The theory evolved from the summability of divergent series (see Borel summation) and treats analytic functions with isolated singularities. He introduced...

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...

series. Summation methods include Cesàro summation, generalized Cesàro ⁠ ( C , α ) {\displaystyle (C,\alpha )} ⁠ summation, Abel summation, and Borel summation...

Euler summable to 1⁄4. The Euler summability also implies Borel summability, with the same summation value, as it does in general. Saichev and Woyczyński arrive...

rates. Renormalons, a possible type of singularity arising when using Borel summation. It is a counterpart of an instanton singularity. A bradyon (or tardyon)...

Borel–Cantelli lemma, Borel–Carathéodory theorem, Heine–Borel theorem, Borel summation, Borel distribution Alexander Borodin, Russian composer and chemist...

convergent summations over a series of other complex functions, as well as understanding when it is possible to apply techniques such as Borel summation, or...

When a formally divergent series in a QFT is summed using Borel summation, the associated Borel transform of the series can have singularities as a function...

Cesàro summation Euler summation Lambert summation Borel summation Summation by parts – transforms the summation of products of into other summations Cesàro...

which summation methods produce the geometric series formula for which common ratios. One application for this information is the so-called Borel-Okada...

anti-Stokes lines meeting at a. Mathematics portal Physics portal Borel summation Berry, M. V. (1988), "Stokes' phenomenon; smoothing a Victorian discontinuity...

Abel summation Cesàro summation Lindelöf summation Euler summation Borel summation Mittag-Leffler summation Lambert summation Euler–Boole summation and...

many summation methods that respect these manipulations and that do assign a "sum" to Grandi's series. Two of the simplest methods are Cesàro summation and...

terms are simply omitted from the summation since P ( A ∣ B n ) {\displaystyle P(A\mid B_{n})} is finite. The summation can be interpreted as a weighted...

higher dimensions. In the latter case, one needs to specify the order of summation, e.g. "a set of uniqueness with respect to summing over balls". To understand...

formal operations on transseries) using accelero-summation, which is a generalization of Borel summation. Transseries can be formalized in several equivalent...

_{\alpha \to 0^{+}}\sum _{n}c_{n}e^{-\alpha n^{2}}.} Abel's theorem Borel summation Zel’Dovich, Y. B. (1961). On the theory of unstable states. Sov. Phys...

choice. The summation is called a periodic summation of the function f {\displaystyle f} . When g T {\displaystyle g_{T}} is a periodic summation of another...