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In this paper we give irrationality results for numbers of the form ∞ n=1 an n! where the numbers a n behave like a geometric progression for a while. The method is elementary, not using differentiation or integration. In particular, we derive elementary proofs of the irrationality of π and e m for Gaussian integers m = 0.
In this paper we study the (ir)rationality of sums ∞
We consider the recently introduced model of low ply graph drawing, a straight-line drawing in which the ply-disks of the vertices do not have many common overlaps, which results in a good distribution of the vertices in the plane. The ply-disk of a vertex is the disk centered at it whose radius is half the length of its longest incident edge. We focus our… (More)
The paper deals with the so-called linearly unrelated sequences. The criterion and the application for irrational sequences and series is included too.
Using an idea of Erd˝ os the paper establishes a criterion for the linear independence of infinite products which consist of rational numbers. A criterion for irrationality is obtained as a consequence.