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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, and new solvable many-body problems
Oksana Bihun, Francesco Calogero
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 genera…
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,…
A new solvable many-body problem of goldfish type
Oksana Bihun, Francesco Calogero
A new solvable many-body problem of goldfish type is introduced and the behavior of its solutions is tersely discussed.
Diophantine properties of the zeros of (monic) polynomials the coefficients of which are the zeros of Hermite polynomials
Oksana Bihun, Francesco Calogero
We introduce a monic polynomial p_N(z) of degree N whose coefficients are the zeros of the N-th degree Hermite polynomial. Note that there are N! such different polynomials p_N(z),…
Properties of the zeros of generalized basic hypergeometric polynomials
Oksana Bihun, Francesco Calogero
We define the generalized basic hypergeometric polynomial of degree in terms of the generalized basic hypergeometric function, which depends on (arbitrary, generic, poss…