2007/12/01 by Alezei Zhedanov, Zhedanov, Alezei · 1 citation
Chemistry · Materials Science · Mathematics · Physics and Astronomy · #33C47 #33E05 #37K10 #Algebraic structures and combinatorial models #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Mathematical functions and polynomials #Molecular spectroscopy and chirality #Nonlinear Optical Materials Research #Nonlinear Waves and Solitons #math.CA #msc:33C47 #msc:33E05 #msc:37K10
paper · pdf · doi:10.48550/arxiv.0712.0058
40 pages, submitted to Ramanujan J
openalex publication_date 2007/12/01 · arxiv created 2010/09/27 · arxiv updated 2010/09/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We construct new elliptic solutions of the restricted Toda chain. These solutions give rise to a new explicit class of orthogonal polynomials which can be considered as a generalization of the Stieltjes-Carlitz elliptic polynomials. Relations between characteristic (i.e. positive definite) functions, Toda chain and orthogonal polynomials are developed in order to derive main properties of these polynomials. The recurrence coefficients and the weight function of these polynomials are expressed explicitly. In the degenerated cases of the elliptic functions the modified Meixner polynomials and the Krall-Laguerre polynomials appear.