Oksana Bihun, Francesco Calogero
Published 2015-10-16Version 1
The notion of generations of monic polynomials such that the coefficients of the polynomials of the next generation coincide with the zeros of the polynomials of the current generation is introduced, and its relevance to the identification of endless sequences of new solvable many-body problems of "goldfish type" is demonstrated.
Bilinear equations and $q$-discrete Painlevé equations satisfied by variables and coefficients in cluster algebras
Diophantine properties of the zeros of (monic) polynomials the coefficients of which are the zeros of Hermite polynomials
Jackson's q-exponential as the exponential of a series
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