Matrix Transormations of Almost Convergent Sequenes. II.
Measure and category---some non-analogues.
Mediations on the product rule.
Mémoire sur les développements en fractions continues de la fonction exponentielle, pouvant servir d'introduction à la théorie des fractions continues algébriques
Mercerian and Tauberian Theorems for Differences.
Méthode directe pour calculer la somme des puissances des premiers nombres entiers
Méthode directe pour calculer la somme des puissances des premiers nombres entiers
Monoides et semi-anneaux complets.
Monoides et semi-anneaux continus.
Monotonicity of segments of harmonic series ( I )
Monotonicity properties of the relative error of a Padé approximation for Mills' ratio.
Multigeometric sequences and Cantorvals
For a sequence x ∈ l 10, one can consider the achievement set E(x) of all subsums of series Σn=1∞ x(n). It is known that E(x) has one of the following structures: a finite union of closed intervals, a set homeomorphic to the Cantor set, a set homeomorphic to the set T of subsums of Σn=1∞ x(n) where c(2n − 1) = 3/4n and c(2n) = 2/4n (Cantorval). Based on ideas of Jones and Velleman [Jones R., Achievement sets of sequences, Amer. Math. Monthly, 2011, 118(6), 508–521] and Guthrie and Nymann [Guthrie...
Nearness of continued fractions.
Nearness relations in linear spaces
In this paper, we consider nearness-based convergence in a linear space, where the coordinatewise given nearness relations are aggregated using weighted pseudo-arithmetic and geometric means and using continuous t-norms.
Necessary and sufficient conditions for joint lower and upper estimates.
Necessary and sufficient Tauberian conditions for the logarithmic summability of functions and sequences
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 , where . (*) 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...
Několik poznámek o řetězcích
New results in discrete asymptotic analysis.
Newer applications of generalized monotone sequences.
Nilakantha's accelerated series for π
We show how the idea behind a formula for π discovered by the Indian mathematician and astronomer Nilakantha (1445-1545) can be developed into a general series acceleration technique which, when applied to the Gregory-Leibniz series, gives the formula with convergence as , in much the same way as the Euler transformation gives with convergence as . Similar transformations lead to other accelerated series for π, including three “BBP-like” formulas, all of which are collected in the Appendix....