21 citations · 68 across the 5 of their papers we have counts for
7 papers
The peculiar (monic) polynomials, the zeros of which equal their coefficients
Francesco Calogero, Francois Leyvraz
We evaluate the number of monic polynomials (of arbitrary degree ) the zeros of which equal their coefficients when these are allowed to take arbitrary complex values. In the fo…
Properties of the zeros of generalized hypergeometric polynomials
Oksana Bihun, Francesco Calogero
We define the generalized hypergeometric polynomial of degree N in terms of the generalized hypergeometric function that depends on p parameters a_1, ..., a_p and q parameters b_1,…
Two novel classes of solvable many-body problems of goldfish type with constraints
Francesco Calogero, David Gomez-Ullate
Two novel classes of many-body models with nonlinear interactions "of goldfish type" are introduced. They are solvable provided the initial data satisfy a single constraint (in one…
Goldfishing by gauge theory
F. Calogero, E. Langmann
A new solvable many-body problem of goldfish type is identified and used to revisit the connection among two different approaches to solvable dynamical systems. An isochronous vari…
Integrable systems of quartic oscillators. II
M. Bruschi, F. Calogero
Several completely integrable, indeed solvable, Hamiltonian many-body problems are exhibited, characterized by Newtonian equations of motion ("acceleration equal force"), with line…
Solvable and/or integrable and/or linearizable N-body problems in ordinary (three-dimensional) space. I
Massimo Bruschi, Francesco Calogero
Several N-body problems in ordinary (3-dimensional) space are introduced which are characterized by Newtonian equations of motion (``acceleration equal force;'' in most cases, the…