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10
Painlevé I asymptotics for orthogonal polynomials with respect to a varying quartic weight
, 2008
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Analysis of nonlinear recurrence relations for the recurrence coefficients of generalized Charlier polynomials
"... The recurrence coe#cients of generalized Charlier polynomials satisfy a system of nonlinear recurrence relations. We simplify the recurrence relations, show that they are related to certain discrete Painleve equations, and analyze the asymptotic behaviour. ..."
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Cited by 7 (4 self)
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The recurrence coe#cients of generalized Charlier polynomials satisfy a system of nonlinear recurrence relations. We simplify the recurrence relations, show that they are related to certain discrete Painleve equations, and analyze the asymptotic behaviour.
qDiscrete Painlevé equations for recurrence coefficients of modified qFreud orthogonal polynomials
, 2008
"... We present an asymmetric qPainlevé equation. We will derive this using qorthogonal polynomials with respect to generalized Freud weights: their recurrence coefficients will obey this qPainlevé equation (up to a simple transformation). We will show a stable method of computing a special solution w ..."
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We present an asymmetric qPainlevé equation. We will derive this using qorthogonal polynomials with respect to generalized Freud weights: their recurrence coefficients will obey this qPainlevé equation (up to a simple transformation). We will show a stable method of computing a special solution which gives the recurrence coefficients. We establish a connection with αqPV. 1
Discrete Painlevé equations for recurrence coefficients of orthogonal polynomials
"... Orthonormal polynomials on the real line are defined by the orthogonality conditions pn(x)pm(x) dµ(x) =δm,n, m,n ≥ 0, (1.1) ..."
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Orthonormal polynomials on the real line are defined by the orthogonality conditions pn(x)pm(x) dµ(x) =δm,n, m,n ≥ 0, (1.1)
unknown title
, 2005
"... Discrete Painlevé equations for recurrence coefficients of orthogonal polynomials ..."
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Discrete Painlevé equations for recurrence coefficients of orthogonal polynomials
unknown title
, 2006
"... Discrete Painlevé equations for recurrence coefficients of orthogonal polynomials ..."
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Discrete Painlevé equations for recurrence coefficients of orthogonal polynomials
1 qDiscrete Painlevé equations for recurrence coefficients of modified qFreud orthogonal polynomials
, 2008
"... We present an asymmetric qPainlevé equation. We will derive this using qorthogonal polynomials with respect to generalized Freud weights: their recurrence coefficients will obey this qPainlevé equation (up to a simple transformation). We will show a stable method of computing a special solution w ..."
Abstract
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We present an asymmetric qPainlevé equation. We will derive this using qorthogonal polynomials with respect to generalized Freud weights: their recurrence coefficients will obey this qPainlevé equation (up to a simple transformation). We will show a stable method of computing a special solution which gives the recurrence coefficients. We establish a connection between the newfound equation and αqPV. 1