On the Atkin Polynomials
Number Theory
2016-01-20 v1 Classical Analysis and ODEs
Abstract
We identify the Atkin polynomials in terms of associated Jacobi polynomials. Our identificationthen takes advantage of the theory of orthogonal polynomials and their asymptotics to establish many new properties of the Atkin polynomials. This shows that co-recursive polynomials may lead to interesting sets of orthogonal polynomials.
Cite
@article{arxiv.1309.2123,
title = {On the Atkin Polynomials},
author = {Ahmad El-Guindy and Mourad E. H. Ismail},
journal= {arXiv preprint arXiv:1309.2123},
year = {2016}
}
Comments
18 pages. Accepted for publication at the Pacific Journal of Mathematics