Functions and Analysis

   

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

Authors: Richard J. Mathar

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.

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

Download: PDF

Submission history

[v1] 2013-03-06 15:32:53
[v2] 2013-03-21 04:33:40

Unique-IP document downloads: 331 times

Vixra.org is a pre-print repository rather than a journal. Articles hosted may not yet have been verified by peer-review and should be treated as preliminary. In particular, anything that appears to include financial or legal advice or proposed medical treatments should be treated with due caution. Vixra.org will not be responsible for any consequences of actions that result from any form of use of any documents on this website.

Add your own feedback and questions here:
You are equally welcome to be positive or negative about any paper but please be polite. If you are being critical you must mention at least one specific error, otherwise your comment will be deleted as unhelpful.

comments powered by Disqus