Multiple orthogonal polynomials (MOPs) extend the classical notion of orthogonality by satisfying simultaneous orthogonality conditions with respect to several weight functions or measures. This ...

A three-complex-parameter class of orthogonal Laurent polynomials on the unit circle associated with basic hypergeometric or q-hypergeometric functions is considered. To be precise, we consider the ...

The intertwined study of orthogonal polynomials and Painlevé equations continues to be a fertile area of research at the confluence of mathematical analysis and theoretical physics. Orthogonal ...

In this paper, we show that for several second-order partial differential equations \begin{align*}L[u] &= A(x,y)u_{xx} + 2B(x,y)u_{xy} + C(x,y)u_{yy} + D(x,y)u_x + E ...