10 citations · 16 across the 4 of their papers we have counts for
4 papers · 1 filter
Writing pi as sum of arctangents with linear recurrent sequences, Golden mean and Lucas numbers
Marco Abrate, Stefano Barbero, Umberto Cerruti +1
In this paper, we study the representation of pi as sum of arcotangents. In particular, we obtain new identities by using linear recurrent sequences. Moreover, we provide a method…
Colored compositions, Invert operator and elegant compositions with the "black tie"
Marco Abrate, Stefano Barbero, Umberto Cerruti +1
This paper shows how the study of colored compositions of integers reveals some unexpected and original connection with the Invert operator. The Invert operator becomes an importan…
Periodic representations and rational approximations of square roots
Marco Abrate, Stefano Barbero, Umberto Cerruti +1
In this paper the properties of Rédei rational functions are used to derive rational approximations for square roots and both Newton and Padé approximations are given as particular…
Construction and Composition of Rooted Trees via Descent Functions
Marco Abrate, Stefano Barbero, Umberto Cerruti +1
We propose a novel approach for studying rooted trees by using functions that we will call descent functions. We provide a construction method for rooted trees that allows to study…