Stanovení součtů jistých nekonečných řad
Summability "au plus petit terme"
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.
Summability of alternations of convergent series.
Summation of series via Laplace transforms.
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
Sur les conditions nécessaires et suffisantes pour que le domaine d'un procédé continu contienne toutes les suites bornées
Sur les séries ordonnées suivant les puissances croissantes d'une variable
Sur un tableau numérique et sur son application à certaines transcendantes