Addition formula for big q-Legendre polynomials
Quantum Algebra
2016-09-06 v1 Classical Analysis and ODEs
Abstract
From Koornwinder's interpretation of big -Legendre polynomials as spherical elements on the quantum group an addition formula is derived for the big -Legendre polynomial. The formula involves Al-Salam--Carlitz polynomials, little -Jacobi polynomials and dual -Krawtchouk polynomials. For the little -ultraspherical polynomials a product formula in terms of a big -Legendre polynomial follows by -integration. The addition and product formula for the Legendre polynomials are obtained when tends to 1.
Keywords
Cite
@article{arxiv.math/9404225,
title = {Addition formula for big q-Legendre polynomials},
author = {Erik Koelink},
journal= {arXiv preprint arXiv:math/9404225},
year = {2016}
}