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Sur quelques développements en séries

E. Catalan (1870)

Nouvelles annales de mathématiques : journal des candidats aux écoles polytechnique et normale

The Lebesgue Constants for Borel Summation of Laplace Series.

Lee Lorch (1981)

Monatshefte für Mathematik

Two valued measure and summability of double sequences

Pratulananda Das, Santanu Bhunia (2009)

Czechoslovak Mathematical Journal

In this paper, following the methods of Connor [connor], we extend the idea of statistical convergence of a double sequence (studied by Muresaleen and Edely [moe]) to $μ$ -statistical convergence and convergence in $μ$ -density using a two valued measure $μ$ . We also apply the same methods to extend the ideas of divergence and Cauchy criteria for double sequences. We then introduce a property of the measure $μ$ called the (APO $_{2}$ ) condition, inspired by the (APO) condition of Connor [jc]. We mainly investigate...

Two-sided averages for which oscillation fails.

Campbell, James T., Jones, Roger L. (2008)

The New York Journal of Mathematics [electronic only]

Ueber die Gauss'sche hypergeometrische Reihe

Schläfli (1871)

Mathematische Annalen

Ueber die höheren hypergeometrischen Reihen, insbesondere über die Reihe: .................................

Thomae (1870)

Mathematische Annalen

Ueber die ungleimässigen Convergenz und die gliedweise Integration der Reihen

W. F. Osgood (1896)

Nachrichten von der Gesellschaft der Wissenschaften zu Göttingen, Mathematisch-Physikalische Klasse

Vector series whose lacunary subseries converge

Lech Drewnowski, Iwo Labuda (2000)

Studia Mathematica

The area of research of this paper goes back to a 1930 result of H. Auerbach showing that a scalar series is (absolutely) convergent if all its zero-density subseries converge. A series $\sum_{n} x_{n}$ in a topological vector space X is called ℒ-convergent if each of its lacunary subseries $\sum_{k} x_{n_{k}}$ (i.e. those with $n_{k + 1} - n_{k} \to \infty$ ) converges. The space X is said to have the Lacunary Convergence Property, or LCP, if every ℒ-convergent series in X is convergent; in fact, it is then subseries convergent. The Zero-Density Convergence...

$μ$ -statistically convergent function sequences

Oktay Duman, Cihan Orhan (2004)

Czechoslovak Mathematical Journal

In the present paper we are concerned with convergence in $μ$ -density and $μ$ -statistical convergence of sequences of functions defined on a subset $D$ of real numbers, where $μ$ is a finitely additive measure. Particularly, we introduce the concepts of $μ$ -statistical uniform convergence and $μ$ -statistical pointwise convergence, and observe that $μ$ -statistical uniform convergence inherits the basic properties of uniform convergence.

Currently displaying 61 – 73 of 73