Orthogonal polynomials on a class of planar algebraic curves

Marco Fasondini, Sheehan Olver, Yuan Xu

We construct bivariate orthogonal polynomials (OPs) on algebraic curves of the form $y^m=\varphi (x)$ in ${\mathbb{R}}^2$ where $m=1,2$ and $\varphi$ is a polynomial of arbitrary degree $d$,…