Numerical integration over a disc. A new Gaussian quadrature formula (Q1267057)

A quadrature formula is constructed for numerical integration over the unit disc \(D:= \{(x,y): x^2+ y^2\leq 1\}\), of the form \[ \iint_D f(x,y)dx dy\approx \sum^n_{k=1} \lambda_k \int_{I_k}f, \] of highest degree of precision with respect to the class of algebraic polynomials of two variables of total degree \(2n-1\), where \(I_k\) are line segments.