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### A summability integral.

Journal für die reine und angewandte Mathematik

### Construction of binomial sums for $\pi$ and polylogarithmic constants inspired by BBP formulas.

Applied Mathematics E-Notes [electronic only]

### Integral Representations of Functional Series with Members Containing Jacobi Polynomials

Mathematica Balkanica New Series

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

Annales Polonici Mathematici

### Le prolongement analytique et les séries sommables

Mathematische Annalen

### Matrix transformations from absolutely convergent series to convergent sequences as general weighted mean summability methods.

International Journal of Mathematics and Mathematical Sciences

### Necessary and sufficient Tauberian conditions for the logarithmic summability of functions and sequences

Studia Mathematica

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 $li{m}_{t\to \infty }\tau \left(t\right)=A$, where $\tau \left(t\right):=1/\left(logt\right){\int }_{1}^{t}s\left(u\right)/udu$. (*) 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.

International Journal of Mathematics and Mathematical Sciences

### On characterization of summability fields by integral

Mathematica Slovaca

### On some convergence tests for series and integrals

Archivum Mathematicum

### On the Numerical Evaluation of a Sum Involving Binomial Coefficients.

Numerische Mathematik

### Remarks on a moment problem and a problem of perfection of power methods of limitation

Colloquium Mathematicae

### Sčítání nekonečných řad pomocí integrálních transformací

Aplikace matematiky

### Statistical extensions of some classical Tauberian theorems in nondiscrete setting

Colloquium Mathematicae

Schmidt’s classical Tauberian theorem says that if a sequence $\left({s}_{k}:k=0,1,...\right)$ 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

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

### The well-behaved Catalan and Brownian averages and their applications to real resummation.

Publicacions Matemàtiques

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.

Mathematische Annalen

### О методе суммирования типа Абеля-Пуассона кратных интегралов Фурье

Matematiceskij sbornik

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