Abstract
We discuss relations between the theory of orthogonal polynomials, Hankel determinants, and the unrestricted one-dimensional Toda chain. In particular, we show that the equations of motion for the Toda chain are equivalent to a Riccati equation for the Stieltjes function. We consider some examples of the Stieltjes function with an explicit (hypergeometric and elliptic) time dependence in detail.
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