# 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