Functions and Analysis

Gaussian Quadrature of the Integrals Int_(-Infty)^infty F(x) dx / Cosh(x)

Authors: Richard J. Mathar
Comments: 10 Pages. Corrected 2 digits in eq. (11). Added remark 2, eqs. (22) and (24), and 2 references

The manuscript delivers nodes and their weights for Gaussian quadratures with a "non-classical" weight in the integrand defined by a reciprocal hyperbolic cosine. The associated monic orthogonal polynomials are constructed; their coefficients are simple multiples of the coefficients of Hahn polynomials. A final table shows the abscissae-weight pairs for up to 128 nodes.
Category: Functions and Analysis