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I-convergence theorems for a class of k-positive linear operators

Mehmet Özarslan (2009)

Open Mathematics

In this paper, we obtain some approximation theorems for k- positive linear operators defined on the space of analytical functions on the unit disc, via I-convergence. Some concluding remarks which includes A-statistical convergence are also given.

Leibniz Series forπ

Karol Pąk (2016)

Formalized Mathematics

In this article we prove the Leibniz series for π which states that π4=∑n=0∞(−1)n2⋅n+1. $\frac{π}{4} = \sum_{n = 0}^{\infty} \frac{{(- 1)}^{n}}{2 \cdot n + 1} .$ The formalization follows K. Knopp [8], [1] and [6]. Leibniz’s Series for Pi is item 26 from the “Formalizing 100 Theorems” list maintained by Freek Wiedijk at http://www.cs.ru.nl/F.Wiedijk/100/.

Linear matrix differential equations of higher-order and applications.

Ben Taher, Rajae, Rachidi, Mustapha (2008)

Electronic Journal of Differential Equations (EJDE) [electronic only]

Local approximation properties of certain class of linear positive operators via I-convergence

Mehmet Özarslan, Hüseyin Aktuǧlu (2008)

Open Mathematics

In this study, we obtain a local approximation theorems for a certain family of positive linear operators via I-convergence by using the first and the second modulus of continuities and the elements of Lipschitz class functions. We also give an example to show that the classical Korovkin Theory does not work but the theory works in I-convergence sense.

Nilakantha's accelerated series for π

David Brink (2015)

Acta Arithmetica

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 $π = \sum_{n = 0}^{\infty} ((5 n + 3) n! (2 n)!) / (2^{n - 1} (3 n + 2)!)$ with convergence as $13 . 5^{- n}$ , in much the same way as the Euler transformation gives $π = \sum_{n = 0}^{\infty} (2^{n + 1} n! n!) / (2 n + 1)!$ with convergence as $2^{- n}$ . Similar transformations lead to other accelerated series for π, including three “BBP-like” formulas, all of which are collected in the Appendix....

Currently displaying 21 – 40 of 60

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Displaying 21 – 40 of 60

I-convergence theorems for a class of k-positive linear operators

Leibniz Series forπ

Linear matrix differential equations of higher-order and applications.

Local approximation properties of certain class of linear positive operators via I-convergence

Nilakantha's accelerated series for π

Note sur une formule de sommation applicable à une classe de séries

Note sur une méthode de transformation des séries, d'après M. Leclert

Notes on two indetities of D. D. Adamović

On a Generalization of the Richardson Extrapolation Process.

On Riemann's theorem about conditionally convergent series

On summations on locally compact spaces

On the dilution of series

On the evaluation of Euler sums.

On the Numerical Evaluation of a Sum Involving Binomial Coefficients.

Optimal Transformations for Scalar Sequences.

Poznámka o řadách nekonečných

Příspěvek k odvozování nekonečných řad a stanovení jich součtů pomocí omezených integralů

Problème sur les équations génératrices des séries récurrentes

Proof of a hypothesis on some segments of harmonic series and a new hypothesis

Ramanujan's harmonic number expansion into negative powers of a triangular number.

Currently displaying 21 – 40 of 60