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Wronskian type determinants of orthogonal polynomials, Selberg type formulas and constant term identities

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Autor: Durán Guardeño, Antonio José
Departamento: Universidad de Sevilla. Departamento de Análisis Matemático
Fecha: 2014-05
Publicado en: Journal of Combinatorial Theory, Series A, 124, 57-96.
Tipo de documento: Artículo
Resumen: Let (pn)n be a sequence of orthogonal polynomials with respect to the measure µ. Let T be a linear operator acting in the linear space of polynomials P and satisfying that deg(T(p)) = deg(p)−1, for all polynomial p. We then construct a sequence of polynomials (sn)n, depending on T but not on µ, such that the Wronskian type n × n determinant det T i−1 (pm+j−1(x)) n i,j=1 is equal to the m × m determinant det q j−1 n+i−1 (x) m i,j=1 , up to multiplicative constants, where the polynomials q i n, n, i ≥ 0, are defined by q i P n(x) = n j=0 µ i j sn−j (x), and µ i j are certain generalized moments of the measure µ. For T = d/dx we recover a Theorem by Leclerc which extends the well-known Karlin and Szeg˝o identities for Hankel determinants whose entries are ultraspherical, Laguerre and Hermite polynomials. For T = ∆, the first order difference operator, we get some very elegant symmetries for Casorati determinants of classical discrete orthogonal polynom...
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Cita: Durán Guardeño, A.J. (2014). Wronskian type determinants of orthogonal polynomials, Selberg type formulas and constant term identities. Journal of Combinatorial Theory, Series A, 124, 57-96.
Tamaño: 388.4Kb
Formato: PDF

URI: http://hdl.handle.net/11441/43014

DOI: http://dx.doi.org/10.1016/j.jcta.2014.01.004

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