Addition formula for 2-parameter family of Askey-Wilson polynomials
Classical Analysis and ODEs
2016-09-06 v1
Abstract
For a two parameter family of Askey-Wilson polynomials, that can be regarded as basic analogues of the Legendre polynomials, an addition formula is derived. The addition formula is a two-parameter extension of Koornwinder's addition formula for the little -Legendre polynomials. A corresponding product formula is derived. As the base tends to one, the addition and product formula go over into the addition and product formula for the Legendre polynomial. The addition formula is derived from the interpretation of Askey-Wilson polynomials as generalised matrix elements on the quantum group.
Keywords
Cite
@article{arxiv.math/9412224,
title = {Addition formula for 2-parameter family of Askey-Wilson polynomials},
author = {Erik Koelink},
journal= {arXiv preprint arXiv:math/9412224},
year = {2016}
}