Elliptic solutions of the Toda chain and a generalization of the Stieltjes-Carlitz polynomials - Mathematics > Classical Analysis and ODEsReportar como inadecuado




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Abstract: We construct new elliptic solutions of the restricted Toda chain. Thesesolutions give rise to a new explicit class of orthogonal polynomials which canbe considered as a generalization of the Stieltjes-Carlitz ellipticpolynomials. Relations between characteristic i.e. positive definitefunctions, Toda chain and orthogonal polynomials are developed in order toderive main properties of these polynomials. The recurrence coefficients andthe weight function of these polynomials are expressed explicitly. In thedegenerated cases of the elliptic functions the modified Meixner polynomialsand the Krall-Laguerre polynomials appear.



Autor: Alezei Zhedanov

Fuente: https://arxiv.org/







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