Geodesic
Toda chain, Stieltjes function, and orthogonal polynomials
Teoretičeskaâ i matematičeskaâ fizika, Tome 151 (2007) no. 1, pp. 81-108

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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.
Keywords: integrable system, Toda chain
Mots-clés : orthogonal polynomial. 
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     title = {Toda chain, {Stieltjes} function, and orthogonal polynomials},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
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F. Peherstorfer; V. P. Spiridonov; A. S. Zhedanov. Toda chain, Stieltjes function, and orthogonal polynomials. Teoretičeskaâ i matematičeskaâ fizika, Tome 151 (2007) no. 1, pp. 81-108. http://geodesic.mathdoc.fr/item/TMF_2007_151_1_a5/