15 citations · 27 across the 9 of their papers we have counts for
9 papers
Systems of several first-order quadratic recursions whose evolution is easily ascertainable
Francesco Calogero
The evolution, as functions of the "ticking time" , of the solutions of the system of quadratic recursions \begin{eqnarray*} x_{n}\left( \ell +1\right) =c_{n}+…
Solvable nonlinear systems of 2 recursions displaying interesting evolutions
Francesco Calogero
In this paper a class of simple, but nonlinear, systems of recursions involving dependent variables is identified, such that the solutions of their init…
Variations on a Theme of Collatz
Mario Bruschi, Francesco Calogero
Consider the recursive relation generating a new positive integer from the positive integer according to the following simple rules: if the integer $n_{\e…
Nonlinear differential algorithm to compute all the zeros of a generic polynomial
Francesco Calogero
A simple algorithm to compute all the zeros of a generic polynomial is proposed.
Finite-dimensional representations of difference operators, and the identification of remarkable matrices
Francesco Calogero
Two square matrices of (arbitrary) order N are introduced. They are defined in terms of N arbitrary numbers z_{n}, and of an arbitrary additional parameter (a respectively q), and…
Properties of the zeros of the polynomials belonging to the q-Askey scheme
Oksana Bihun, Francesco Calogero
In this paper we provide properties -- which are, to the best of our knowledge, new -- of the zeros of the polynomials belonging to the q-Askey scheme. These findings include Dioph…