Functions and Analysis

    

On a Specific Family of Orthogonal Polynomials of Bernstein-Szego Type

Authors: Martin Nicholson

We study a class of weight functions on [-1,1] which are special cases of the broader family studied by Bernstein and Szego. These weights are parametrized by two positive integers. As these integers tend to infinity, these weights approximate certain weight functions on R considered by Ismail and Valent. We also study modifications of these weight functions by a continuous parameter a>0. These ideas are then used to find finite analogs of some improper integrals first studied by Glaisher and Ramanujan. We also show that some of the functions used in this work are in fact generating functions of certain finite trigonometric sums.

Comments: 15 Pages.

Download: PDF

Submission history

[v1] 2025-05-08 20:01:59
[v2] 2025-07-02 08:08:56

Unique-IP document downloads: 342 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