Product Gaussian Quadrature on Circular Lunes

Abstract

Resorting to recent results on subperiodic trigonometric quadrature, we provide three product Gaussian quadrature formulas exact on algebraic polynomials of degree $n$ on circular lunes. The first works on any lune, and has $n^2 + \mathcal{O}(n)$ cardinality. The other two have restrictions on the lune angular intervals, but their cardinality is $n^2/2 + \mathcal{O}(n)$.