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Orthogonal polynomials on the unit circle satisfying a second-order differential equation with varying polynomial coefficients

Borrego-Morell, J. ; Sri Ranga, A.

Integral transforms and special functions, 2017-01, Vol.28 (1), p.39-55 [Periódico revisado por pares]

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Título:
Orthogonal polynomials on the unit circle satisfying a second-order differential equation with varying polynomial coefficients
Autor: Borrego-Morell, J. ; Sri Ranga, A.
Assuntos: 30Axx ; complex analysis ; differential equations ; Orthogonal polynomials on the unit circle ; special functions
É parte de: Integral transforms and special functions, 2017-01, Vol.28 (1), p.39-55
Descrição: Consider the linear second-order differential equation (1.1) where with or , are polynomials with complex coefficients and . Under some assumptions over a certain class of lowering and raising operators, we show that for a sequence of polynomials orthogonal on the unit circle to satisfy the differential equation ( 1.1 ), the polynomial must be of a specific form involving and extension of the Gauss and confluent hypergeometric series.
Editor: Abingdon: Taylor & Francis
Idioma: Inglês

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