A summability integral.
Construction of binomial sums for and polylogarithmic constants inspired by BBP formulas.
Integral Representations of Functional Series with Members Containing Jacobi Polynomials
MSC 2010: Primary 33C45, 40A30; Secondary 26D07, 40C10In this article we establish a double definite integral representation, and two other indefinite integral expressions for a functional series and its derivative with members containing Jacobi polynomials.
Integral transformations and closed form expressions for sums of double infinite series
Le prolongement analytique et les séries sommables
Matrix transformations from absolutely convergent series to convergent sequences as general weighted mean summability methods.
Necessary and sufficient Tauberian conditions for the logarithmic summability of functions and sequences
Let s: [1,∞) → ℂ be a locally Lebesgue integrable function. We say that s is summable (L,1) if there exists some A ∈ ℂ such that , where . (*) It is clear that if the ordinary limit s(t) → A exists, then also τ(t) → A as t → ∞. We present sufficient conditions, which are also necessary, in order that the converse implication hold true. As corollaries, we obtain so-called Tauberian theorems which are analogous to those known in the case of summability (C,1). For example, if the function s is slowly...
Norm-preserving L-L integral transformations.
On characterization of summability fields by integral
On some convergence tests for series and integrals
On the Numerical Evaluation of a Sum Involving Binomial Coefficients.
Remarks on a moment problem and a problem of perfection of power methods of limitation
Sčítání nekonečných řad pomocí integrálních transformací
Statistical extensions of some classical Tauberian theorems in nondiscrete setting
Schmidt’s classical Tauberian theorem says that if a sequence of real numbers is summable (C,1) to a finite limit and slowly decreasing, then it converges to the same limit. In this paper, we prove a nondiscrete version of Schmidt’s theorem in the setting of statistical summability (C,1) of real-valued functions that are slowly decreasing on ℝ ₊. We prove another Tauberian theorem in the case of complex-valued functions that are slowly oscillating on ℝ ₊. In the proofs we make use of two nondiscrete...
Summability factors for generalized absolute Riesz summability I
The well-behaved Catalan and Brownian averages and their applications to real resummation.
The aim of this expository paper is to introduce the well-behaved uniformizing averages, which are useful in resummation theory. These averages associate three essential, but often antithetic, properties: respecting convolution; preserving realness; reproducing lateral growth. These new objects are serviceable in real resummation and we sketch two typical applications: the unitary iteration of unitary diffeomorphisms and the real normalization of real, local, analytic, vector fields.
Weighted Versions of Beurling's Tauberian Theorem.
О методе суммирования типа Абеля-Пуассона кратных интегралов Фурье