Mengkun Zhu

collaborators

3 papers

math.CA2026

PainlevÃ© IV, bi-confluent Heun equations and the Hankel determinant generated by a discontinuous semi-classical Laguerre weight

Mengkun Zhu, Jianduo Yu

We consider the discontinuous semi-classical Laguerre weight function with a jump $w (x; t, s) = e^{- x^{2} + t x} (A + B I^¸ (x - s))$ , where $x \in R$ , $t, s \geq 0$ , $A \geq 0$ , $A + B \geq 0$ …

math.CA2025

Recurrence coefficients for the time-evolved Jacobi weight and discrete PainlevÃ© equations on the $D_{5}$ Sakai surface

Mengkun Zhu, Siqi Chen, Xuhao Zhang

In this paper, we focus on the relationship between the d-P $(A_{3}^{(1)} / D_{5}^{(1)})$ equations and a time-evolved Jacobi weight, $w (x) = x^{I^} \pm (1 - x)^{2} e^{- s x}$ , $…

math.CA2025

Recurrence coefficients for the semiclassical Laguerrre weight and d-P $(A_{2}^{(1)} / E_{6}^{(1)})$ equations

Siqi Chen, Mengkun Zhu

In this paper, we use Sakai's geometric framework to explore the profound interconnection between recurrence coefficients of the semiclassical Laguerre weight $w(x)=x^Î»\mathrm{e}^…

PainlevÃ© IV, bi-confluent Heun equations and the Hankel determinant generated by a discontinuous semi-classical Laguerre weight

Recurrence coefficients for the time-evolved Jacobi weight and discrete PainlevÃ© equations on the D5​ Sakai surface

Recurrence coefficients for the semiclassical Laguerrre weight and d-P(A2(1)​/E6(1)​) equations

Recurrence coefficients for the time-evolved Jacobi weight and discrete PainlevÃ© equations on the $D_{5}$ Sakai surface

Recurrence coefficients for the semiclassical Laguerrre weight and d-P $(A_{2}^{(1)} / E_{6}^{(1)})$ equations