Partial differential equations (PDEs) are used with huge success to model phenomena
across all scientific and engineering disciplines. However, across an equally wide swath …

We review recent advances in algorithms for quadrature, transforms, differential equations
and singular integral equations using orthogonal polynomials. Quadrature based on …

This paper presents a method for accurate and efficient computations on scalar, vector and
tensor fields in three-dimensional spherical polar coordinates. The method uses spin …

We describe fast algorithms for approximating the connection coefficients between a family
of orthogonal polynomials and another family with a polynomially or rationally modified …

We present cunuSHT, a general-purpose Python package that wraps a highly efficient
CUDA implementation of the non-uniform spin-0 spherical harmonic transform. The method …

In this paper, we demonstrate that many of the computational tools for univariate orthogonal
polynomials have analogues for a family of bivariate orthogonal polynomials on the triangle …

We introduce a method to numerically compute equilibrium measures for problems with
attractive-repulsive power law kernels of the form $ K (xy)=\frac {| xy|^\alpha}{\alpha}-\frac …

We present explicit constructions of orthogonal polynomials inside quadratic bodies of
revolution, including cones, hyperboloids, and paraboloids. We also construct orthogonal …

We prove and collect numerous explicit and computable results for the fractional Laplacian
$(-\Delta)^ sf (x) $ with $ s> 0$ as well as its whole space inverse, the Riesz potential …

In recent years, sparse spectral methods for solving partial differential equations have been
derived using hierarchies of classical orthogonal polynomials (OPs) on intervals, disks, disk …