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Remarks on several types of convergence of bounded sequences

Vladimír Baláž, Oto Strauch, Tibor Šalát (2006)

Acta Mathematica Universitatis Ostraviensis

In this paper we analyze relations among several types of convergences of bounded sequences, in particulars among statistical convergence, u -convergence, ϕ -convergence, almost convergence, strong p -Cesàro convergence and uniformly strong p -Cesàro convergence.

Summability "au plus petit terme"

María-Angeles Zurro (1995)

Studia Mathematica

There is a curious phenomenon in the theory of Gevrey asymptotic expansions. In general the asymptotic formal power series is divergent, but there is some partial sum which approaches the value of the function very well. In this note we prove that there exists a truncation of the series which comes near the function in an exponentially flat way.

Summation of series via Laplace transforms.

Anthony Sofo (2002)

Revista Matemática Complutense

We consider a forced differential difference equation and by the use of Laplace Transform Theory generate non-hypergeometric type series which we prove may be expressed in closed form.

Sur la série harmonique

E. Cesàro (1885)

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

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