Publicação: Orthogonal polynomials on the unit circle satisfying a second-order differential equation with varying polynomial coefficients
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Taylor & Francis Ltd
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Consider the linear second-order differential equation An(z) y+ B-n(z) y' + C(n)y = 0, where A(n)(z) = a(2), nz(2) + a(1,n)z + a(0), n with a(2), n = 0, a2 1, n - 4a2, na0, n = 0,. n. N or a2, n = 0, a1, n = 0,. n. N, Bn(z) = b1, n + b0, nz are polynomials with complex coefficients and Cn. C. Under some assumptions over a certain class of lowering and raising operators, we show that for a sequence of polynomials (fn)8 n = 0 orthogonal on the unit circle to satisfy the differential equation (1.1), the polynomial fn must be of a specific form involving and extension of the Gauss and confluent hypergeometric series.
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Orthogonal polynomials on the unit circle, differential equations, special functions, complex analysis
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Inglês
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Integral Transforms And Special Functions. Abingdon: Taylor & Francis Ltd, v. 28, n. 1, p. 39-55, 2016.
