Numerical Application of Euler's Series Transformation and its Generalizations.
On some quadrature rules with Laplace end corrections
We investigate quadrature rules with Laplace end corrections that depend on a parameter β. Specific values of β yield sixth order rules. We apply our results to approximating the sum of slowly converging series s = Σi=1∞ f(i + 1/2) where f ∈ C 6 with its sixth derivative of constant sign on [m, ∞) and ∫ m∞ f(x)dx is known for m ∈ ℕ. Several examples show the efficiency of this method. This paper continues the results from [Solak W., Szydełko Z., Quadrature rules with Gregory-Laplace end corrections,...
On some transforms of trigonometric series.
On the Acceleration of Limit Periodic Continued Fractions.
On Two Methods for Accelerating Convergence of Series.
Repeated Modifications of Limit k-Periodic continued Fractions.
Resommation des series formelles. Solutions d'équations différentielles linéaires ordinaires du second ordre dans le champ complexe au voisinage de singularités irrégulières.
Résultats négatifs en accélération de la convergence.
Series para e de gran convergenica
Some Generalizations of the Euler-Knopp Transformation.
Some new formulas for .
Some remarks on -faster convergent infinite series
A structure of terms of -faster convergent series is studied in the paper. Necessary and sufficient conditions for the existence of -faster convergent series with different types of their terms are proved. Some consequences are discussed.
Spolehlivost numerických výpočtů
Stable Convergence Acceleration Using Laplace Transforms.
Summation of series by some substitutions
Summation of slowly convergent series
Among the applications of orthogonal polynomials described briefly on my previous visit to this Center [9, §3.2] were slowly convergent series whose terms could be represented in terms of the Laplace transform at integer arguments. We proposed to sum such series by means of Gaussian quadrature rules applied to suitable integrals involving weight functions of Einstein and Fermi type (cf. [13]). In the meantime it transpired that the technique is applicable to a large class of numerical series and,...
The e-Algorithm and Multivariate Pade-Approximants
The high-precision summation of series whose terms are rational numbers
The Weierstrass Mean. I. The periods of ...(z|e1, e2, e3).
Transcendence of infinite sums of simple functions