Polynomials Satisfying Functional and Differential Equations and Diophantine Properties of Their Zeros

By investigating the behavior of two solvable isochronous N-body problems in the immediate vicinity of their equilibria, functional equations satisfied by the para-Jacobi poly- nomial pN (0,1; γ ; x) and by the Jacobi polynomial P (−N −1,−N −1) N (x) (or, equivalently, by the Gegenbauer polynomial C −N −1/2 N (x)) are identified, as well as Diophantine properties of the zeros and coefficients of these polynomials