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Teoreticheskaya i Matematicheskaya Fizika, 2007, Volume 151, Number 1, Pages 81–108
DOI: https://doi.org/10.4213/tmf6013 (Mi tmf6013) 		 
This article is cited in 21 scientific papers (total in 21 papers)

Toda chain, Stieltjes function, and orthogonal polynomials

F. Peherstorfera, V. P. Spiridonovb, A. S. Zhedanovc

a Johannes Kepler University Linz
b Joint Institute for Nuclear Research
c Donetsk Physical-Technical Institute, National Academy of Sciences of Ukraine
Full-text PDF (557 kB) Citations (21)
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DOI: https://doi.org/10.4213/tmf6013
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.
Keywords: integrable system, Toda chain, orthogonal polynomial.
Received: 29.08.2006
English version:
Theoretical and Mathematical Physics, 2007, Volume 151, Issue 1, Pages 505–528
DOI: https://doi.org/10.1007/s11232-007-0038-8
Bibliographic databases:
Language: Russian
Citation: F. Peherstorfer, V. P. Spiridonov, A. S. Zhedanov, “Toda chain, Stieltjes function, and orthogonal polynomials”, TMF, 151:1 (2007), 81–108; Theoret. and Math. Phys., 151:1 (2007), 505–528
Citation in format AMSBIB
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    • This publication is cited in the following 21 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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