Shulin Lyu

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20242026

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math-ph2026

Recurrence Coefficients of the Orthogonal Polynomials for Oscillatory Jacobi-type Weight Functions

Shulin Lyu, Xun Zhou

We study two classes of oscillatory Jacobi-type weight functions $x^{c} (1 - x^{2})^{I^» - 1/2} exp (i I^¶ x)$ , $x \in [- 1, 1], I^» > - 1/2, c \in {0, 1}$ . Other restrictions are imposed on $I^»$ and $Î¶…

math-ph2026

Hankel Determinant for a Perturbed Laguerre Weight with Pole Singularities and Generalized PainlevÃ© III' Equation

Shulin Lyu, Yuanfei Lyu

We study the Hankel determinant for the weight $x^{I^} \pm exp (- x - t_{1} / x - t_{2} / x^{2}), x \in [0, + \infty)$ , with $I^\pm > - 1, t_{1} \in R ∖ {0}, t_{2} > 0.$ Compared with the weight $x…

math-ph2024

Hankel Determinants for a Deformed Laguerre Weight with Multiple Variables and Generalized PainlevÃ© V Equation

Xinyu Mu, Shulin Lyu

We study the Hankel determinant generated by the moments of the deformed Laguerre weight function $x^{I^} \pm e^{- x} k = 1 \prod N (x + t_{k})^{I^»_{k}}$ , where $x\in \left[0,+\inf…

math-ph2024

Yang Chen, Shulin Lyu

We study the Hankel determinant generated by the Gaussian weight with jump discontinuities at $t_{1}, \dots, t_{m}$ . By making use of a pair of ladder operators satisfied by the associa…

math-ph2024

Shengjie Zhang, Shulin Lyu

We consider the Hankel determinant generated by the moments of the even weight function $e^{- x^{2}} (A + B I^¸ (x^{2} - a^{2})), x \in (- \infty, + \infty), a > 0, A \geq 0, A + B \geq 0$ . It is intimate…

Recurrence Coefficients of the Orthogonal Polynomials for Oscillatory Jacobi-type Weight Functions

Hankel Determinant for a Perturbed Laguerre Weight with Pole Singularities and Generalized PainlevÃ© III' Equation

Hankel Determinants for a Deformed Laguerre Weight with Multiple Variables and Generalized PainlevÃ© V Equation

Gaussian Unitary Ensembles with Jump Discontinuities, PDEs and the Coupled PainlevÃ© IV System

Gap Probability Distribution of Gaussian Unitary Ensembles and PainlevÃ© V Equation