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- Title
The Recurrence Coefficients of Orthogonal Polynomials with a Weight Interpolating between the Laguerre Weight and the Exponential Cubic Weight.
- Authors
Min, Chao; Fang, Pixin
- Abstract
In this paper, we consider the orthogonal polynomials with respect to the weight w (x) = w (x ; s) : = x λ e − N [ x + s (x 3 − x) ] , x ∈ R + , where λ > 0 , N > 0 and 0 ≤ s ≤ 1 . By using the ladder operator approach, we obtain a pair of second-order nonlinear difference equations and a pair of differential–difference equations satisfied by the recurrence coefficients α n (s) and β n (s) . We also establish the relation between the associated Hankel determinant and the recurrence coefficients. From Dyson's Coulomb fluid approach, we prove that the recurrence coefficients converge and the limits are derived explicitly when q : = n / N is fixed as n → ∞ .
- Subjects
ORTHOGONAL polynomials; NONLINEAR difference equations; DIFFERENTIAL-difference equations; DIFFERENCE equations
- Publication
Mathematics (2227-7390), 2023, Vol 11, Issue 18, p3842
- ISSN
2227-7390
- Publication type
Article
- DOI
10.3390/math11183842