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We give a systematic presentation of the sequence in the title, characterizing it and showing its properties and its role in several areas: the nature of some series, with a closed form for its n-th partial sum, the Wallis "domain" (his integrals, formula and inequality), some limits obtained in an elementary way using this sequence, some definite integrals, its deep link with the gamma function, its role in certain Taylor-Maclaurin expansions. We also cite some converse assertions of Professor Alexandru Lupas which characterize the sequence and remember in a certain manner, but in the discrete domain, the famous theorem of Bohr-Mollerup. [ABSTRACT FROM AUTHOR]

In this work we present a generalization of the operator of Lupaş [6]. [ABSTRACT FROM AUTHOR]

The presentation consists in a remembering of the life and the work of our beloved master Acad. Prof. D. D. Stancu. [ABSTRACT FROM AUTHOR]

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 the differential calculus, the other is probably the most natural. We recall the situation of the monotony in the general case of (1+1/n) n+p, we point out the order of convergence of (1+/n) n+0.5 and we show how the monotony of the considered sequence can be used to obtain the shortest proof of the weak form of Stirling's formula. [ABSTRACT FROM AUTHOR]

We give a view about the rationality or the irrationality of the real numbery xy, with x,y ∊R, x>0, with a special pointing out of the most interesting case where x and y are both irrational. We show how we can avoid the use of a theorem of A. O. Ghelfond and after presenting the propositions 1 and 2 we give a discussion about the use of the aristotelic principle "tertium non datur" and the intuitionostic point of vue of Luitzen E. J. Brouwer. [ABSTRACT FROM AUTHOR]

The study of any nontrivial convergence of a sequence of real numbers conducts to the problem of finding the limit but also to the problem of the speed of this convergence. This speed of convergence is characterized by the first iterated limit (that supposes the existence of a function of natural variable that tends to zero for n tending to infinity, a function that appears as the first term of a sequences of such functions). A significant characterization of the first iterated limit may be given by a two sided estimate, from which the first iterated limit results immediately. [ABSTRACT FROM AUTHOR]

Starting from some older ideas of [12] and [6], we show new facts concerning the approximation of the constant of Napier. [ABSTRACT FROM AUTHOR]