Functions and Analysis

1303 Submissions

[2] viXra:1303.0038 [pdf] replaced on 2013-03-21 04:33:40

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

[1] viXra:1303.0013 [pdf] replaced on 2013-10-02 14:02:55

Gauss-Laguerre and Gauss-Hermite Quadrature on 64, 96 and 128 Nodes

Authors: Richard J. Mathar
Comments: 27 Pages. Tables extended to Hermite quadratures for x^m*exp(-x^2), m=2, 4, 6 or 8.

The manuscript provides tables of abscissae and weights for Gauss-Laguerre integration on 64, 96 and 128 nodes, and abscissae and weights for Gauss-Hermite integration on 96 and 128 nodes.
Category: Functions and Analysis