# On the Convergence of the Sequence Defining Euler's Number

## Related Articles

- e // Hutchinson Dictionary of Scientific Biography;2005, p1
Symbol for

Euler's number . - An Extension of the Beale-Kato-Majda Criterion for the Euler Equations. Planchon, Fabrice // Communications in Mathematical Physics;Jan2003, Vol. 232 Issue 2, p319
The Beale-Kato-Majda criterion asserts that smooth solutions to the Euler equations remain bounded past T as long as âˆ«0T â€–Ï‰ â€–âˆˆdt is finite, Ï‰ being the vorticity. We show how to replace this by a weaker statement, on supj âˆ«0T â€–Î”jÏ‰...

- A fresh look at Euler's limit formula for the gamma function. JAMESON, G. J. O. // Mathematical Gazette;Jul2014, Vol. 98 Issue 542, p235
The article focuses on Euler's limit formula that plays an essential part in the theory of the gamma function. Topics covered include an alternative method for the real case based on the fact that a sequence is convergent if it is increasing and bounded above, proof of the Bohr-Mollerup theorem...

- ON THE MONOTONY OF (1+1/n) n+0.5 AND AN APPLICATION. VERNESCU, ANDREI // Journal of Science & Arts;2013, Vol. 13 Issue 3, p261
In this paper we expose two different proofs for the fact that the sequence of general term (1+1/n) n+0.5which converges to the celebrated constant of Napier also called the number of Euler, the number e, is strictly decreasing. The one of the proofs shows the possibility of work without to use...

- EULER, LAMBERT, AND THE LAMBERT W-FUNCTION TODAY. Brito, P. B.; Fabião, F.; Staubyn, A. // Mathematical Scientist;Dec2008, Vol. 33 Issue 2, p127
The Lambert W-function has found applications in an extraordinary number of scientific fields. In this paper we present a short historical review, a brief description of the function, and a survey of some of its applications.

- Multivariate Interpolation Functions of Higher-Order q-Euler Numbers and Their Applications. Ozden, Hacer; Cangul, Ismail Naci; Simsek, Yilmaz // Abstract & Applied Analysis;2008, p1
The aim of this paper, firstly, is to construct generating functions of q-Euler numbers and polynomials of higher order by applying the fermionic p-adic q-Volkenborn integral, secondly, to define multivariate q-Euler zeta function (Barnes-type Hurwitz q-Euler zeta function) and l-function which...

- On the mean value of some new sequences. Jiao Chen // Scientia Magna;2010, Vol. 6 Issue 4, p29
The main purpose of this paper is using the elementary and analytic methods to study the mean value properties of the Smarandache repetitional sequence, and give two asymptotic formulas for it.

- An Explicit One-Step Method for Stiff Problems. Novati, P. // Computing;2003, Vol. 71 Issue 2, p133
In this paper we introduce an explicit one-step method that can be used for solving stiff problems. This method can be viewed as a modification of the explicit Euler method that allows to reduce the stiffness in some sense. Some numerical experiments on linear stiff problems and on the Van der...

- On Eulerâ€™s hypothetical proof. Mačys, J. // Mathematical Notes;Oct2007, Vol. 82 Issue 3/4, p352
It is conjectured that Euler possessed an elementary proof of Fermatâ€™s theorem for n = 3. In this note, we show that this opinion is rather credible, because, from Eulerâ€™s results, one can obtain an elementary proof of the nonexistence of positive integer solutions of the equation...