Fully symmetric interpolatory rules for multiple integrals over infinite regions with Gaussian weight

In this paper, the following multiple fractional part integrals I n , β α 1 , α 2 , , α n = 0 , 1 n j = 1 n x j α j { S n - 1 } β d x 1 d x n and J n , β α = 0 , 1 n S n α { S n - 1 } β d x 1 d x n are studied for positive integer n and complex values ...

It is well known that Gaussian cubature rules are related to multivariate orthogonal polynomials. The cubature rules found in the literature use common zeroes of some linearly independent set of products of basically univariate polynomials. We show how ...

In this work, we derive a family of symmetric numerical quadrature formulas for finite-range integrals I[f]=@!"-"1^1w(x)f(x)dx, where w(x) is a symmetric weight function. In particular, we will treat the commonly occurring case of w(x)=(1-x^2)^@a[log(1-...