Gauss Type Quadrature Formula for Fourier Integral

Asymptotic Error Estimates for the Gauss Quadrature Formula

Gauss-type Quadrature Rules for Rational Functions

When integrating functions that have poles outside the interval of integration, but are regular otherwise, it is suggested that the quadrature rule in question ought to integrate exactly not only polynomials (if any), but also suitable rational functions. The latter are to be chosen so as to match the most important poles of the integrand. We describe two methods for generating such quadrature ...

The Combinatorial Gauss Diagram Formula for Kontsevich Integral

In this paper, we shall give an explicit Gauss diagram formula for the Kontsevich integral of links up to degree four. This practical formula enables us to actually compute the Kontsevich integral in a combinatorial way.

Sine Function Quadrature Rules for the Fourier Integral

In this paper a numerical algorithm is proposed for the computation of the Fourier Transform. The quadrature rule developed is based on the Whittaker Cardinal Function expansion of the integrand and a certain Conformai Map. The error of the method is analyzed and numerical results are reported which confirm the accuracy of the quadrature rule.

Gauss Type Quadrature Rules for Cauchy Principal Value Integrals

Two quadrature rules for the approximate evaluation of Cauchy principal value integrals, with nodes at the zeros of appropriate orthogonal polynomials, are discussed. An expression for the truncation error, in terms of higher order derivatives, is given for each rule. In addition, two theorems, containing sufficient conditions for the convergence of the sequence of quadrature rules to the integ...