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- W2010025216 abstract "In this paper we derive the nonlinear recurrence relation for the recursion coefficients βn of polynomials orthogonal with respect to q-analogues of Freud exponential weights. An asymptotic relation for βn is given under assuming a certain smoothing condition and the Plancherel–Rotach asymptotic for the corresponding orthogonal polynomials is derived. Special interest is paid to the case m=2. We prove that the nonlinear recurrence relation of βn in this case obeys the discrete Painlevé property. Motivated by Lew and Quarles, we study possible periodic solutions for a class of nonlinear difference equations of second order. Finally we prove that the Bernstein approximation problem associated to the weights under consideration has a positive solution." @default.
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- W2010025216 date "2010-10-01" @default.
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- W2010025216 title "q-Analogues of Freud weights and nonlinear difference equations" @default.
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- W2010025216 doi "https://doi.org/10.1016/j.aam.2010.02.003" @default.
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